Calibration of a surveying instrument

ABSTRACT

A method for calibrating a surveying instrument is disclosed, the survey instrument comprising a base element and a camera with an image sensor, the camera being rotatable about a vertical axis fixed with respect to said base element and being rotatable about a tilting axis, the tilting axis being rotated about the vertical axis with rotation of the camera about the vertical axis. In the method, data associated with calibration points and images of the calibration points on the image sensor captured in different faces are used, the data for each of said calibration points comprising distance data and the data for each of the images of each said calibration point comprising image position data and orientation data. Further, on the basis of the distance data for each of the calibration points and the image position and orientation data for each of the images of the calibration points the surveying instrument is calibrated simultaneously taking into account at least one optical property of the camera and at least one of the relative orientation of the vertical axis and the tilting axis and the orientation of the camera relative to one of the base element, the vertical axis and the tilting axis.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.10/581,480 filed Jun. 1, 2006, which was the National Stage ofInternational Application No. PCT/EP2004/014365 filed Dec. 16, 2004, theentire contents of which is incorporated herein by reference.

The present invention relates to a method for calibrating a surveyinginstrument comprising a camera, means for carrying out the method andsurveying instruments calibrated by use of the method.

Surveying often includes determination of angles or of positions ofpoints, e.g. reflectors (triple reflectors) or targets in the terrain.Those angles or positions may be measured by surveying instruments suchas theodolites or tacheometers.

Positions in space can be defined by coordinates in a suitablecoordinate system. For example, the position of a point may be definedby its Cartesian coordinates which are defined with respect to aCartesian coordinate system having three axes which are orthogonal toeach other. For measuring positions, however, spherical coordinates aremore appropriate. As shown in FIG. 1, the position of a point may bedefined in spherical coordinates by its distance d to the origin of anorthogonal coordinate system, an angle a between one of the horizontalaxes of the coordinate system and a line connecting the origin of thecoordinate system with a projection of the point onto the horizontalplane and finally a vertical angle θ between the coordinate system axisorthogonal to the horizontal plane and a line connecting the origin ofthe coordinate system and the point. As well known in the art, Cartesiancoordinates can be transformed into spherical coordinates and viceversa.

Surveying instruments such as theodolites or tacheometers, also known astachymeters or total stations, make use of spherical coordinates. Asschematically shown in FIG. 1, known theodolites or tacheometerscomprise a telescope 1 which is rotatable about a vertical axis 2 whichis fixed to a base element 3 of the theodolite or tacheometer and atilting axis 4 which is rotated with rotation of a telescope 1 about thevertical axis 2. Angles of rotation about the vertical axis 2 and anglesof tilting about the tilting axis can read from a correspondinghorizontal circle 5 and a vertical circle 6.

In an ideal theodolite or tacheometer, the tilting axis 4 is orthogonalto the vertical axis 2 and both axes intersect in one point. Further, aline of the sight 7 of the telescope 1, also called sighting axis orsight axis, is orthogonal to the tilting axis 4 and further runs throughthe intersection point of the tilting axis 4 and the vertical axis 2.For measuring the position of a point, ideally, the theodolite ortacheometer is oriented such that the vertical axis 2 is perfectlyperpendicular, i.e. it points in the direction of gravity. Then, aspherical coordinate system can be defined by a plane orthogonal to thevertical axis 2 and the vertical axis 2, the origin being theintersection point of the of the tilting axis 4 and by the vertical axis2. By the horizontal circle 5 one axis of the coordinate system can bedefined which is fixed with respect to the base element 3. For measuringthe above-mentioned angles α and θ the sighting axis 7 of a telescope 1is directed to the point to be measured by rotating the telescope 1about the vertical axis 2 and tilting the telescope 1 about the tiltingaxis 4. The angle α can than be read from the horizontal circle and theangle θ from the vertical circle 6. Knowing the distance of the pointfrom the instrument, the Cartesian coordinates can be easily obtained.

Practically, however, the above-mentioned conditions for an idealtheodolite or tacheometer are not met. Rather, the accuracy ofmeasurements may be reduced by different types of errors. A first errorrelates to the orientation of the vertical axis 2. It should beperfectly perpendicular to the ground, i.e. it should point along thedirection of gravity, but in practice it may not be so. This error isnot caused by the instrument itself and thus can only be avoided byproper orientation of the surveying instrument. As second error, aline-of-sight error or collimation error may occur which is a deviationof the angle γ between the sighting axis 7 and the tilting axis 4 from aright angle (see FIG. 2A). A third error is the so called tilting-axiserror (see FIG. 2B) which is the deviation of the angle between thetilting axis and the vertical axis from a right angle. Finally, a socalled height-index error z₀ may occur which is the deviation betweenthe true angle between the sighting axis and the vertical axis and thecorresponding angle read on the vertical circle (see FIG. 2C). Theselast three errors are caused by tolerances of the surveying instrument.In order to be able to provide correct measurements, the surveyinginstrument needs to be calibrated, that is a relationship between theangles read on the horizontal and vertical circles and the correspondingtrue angles has to be established.

So called video-theodolites or video-tacheometers differ fromtraditional theodolites or tacheometers in that they comprise a camerawhich may for example replace the whole telescope or just the eyepieceof the telescope. As schematically shown in FIG. 3, the camera 8comprises an optical system 9 and an image sensor 10. The optical system9 forms images of points in a scene on the image sensor 10. A point tobe measured is thus imaged onto a certain position on the image sensor10. In order to determine from the position of the image of the point onthe image sensor a direction from the surveying instrument to the point,the direction being defined by true vertical and horizontal angles, oneneeds to know the relationship between a position on the image sensorand a corresponding direction in space.

The optical axis of an ideal camera should be perpendicular to the planeof the image sensor and the optical system should be free of aberrationsor distortions. Further, the optical axis should be parallel to areference axis of the camera.

However, real cameras do not have these ideal properties. Thus, acalibration, i.e. a mapping between directions in space andcorresponding positions of images of these directions on the imagesensor, is necessary.

In the case of surveying instruments having a camera such asvideo-theodolites or video-tacheometers at least two calibrations appearto be necessary, namely one with respect to the axes of the instrumentand the other with respect to the camera.

In an article by Y. D. Huang, “Calibration of the Wild P32 Camera usingthe Camera-ON-Theodolite method”, published in Photogrammetric Record,16(91), 1998, Huang connects one or at most two reference pointsarranged at different distances to the instrument, that is the systemconsisting of the surveying instrument proper and the camera. Thesereference points are observed with the camera to be calibrated atdifferent instrument directions, i.e. different combinations ofhorizontal and vertical angles to be set on the instrument. As Huanguses a theodolite, the distance between the two points, or the distancebetween the points and the instrument must be known. A further drawbackof Huang's method is that instrument errors such as vertical axis errorsand lateral collimation errors remain out of consideration. However,calibration errors increase with the magnitude of these instrumenterrors, which diminishes the overall accuracy of the instrument.

Thus, it is an object underlying the invention to provide a method forcalibrating a surveying instrument having a camera, in particular avideo-theodolite or a video-tacheometer, the method being easy toperform and requiring only little information about the surveyinginstrument, and to provide means for executing the method.

According to a first aspect of the invention a method is provided forcalibrating a surveying instrument comprising a base element and acamera with an image sensor, the camera being rotatable about a verticalaxis fixed with respect to said base element and being rotatable about atilting axis, the tilting axis being rotated about the vertical axiswith rotation of the camera about the vertical axis, wherein dataassociated with calibration points and images of the calibration pointson the image sensor captured in different faces are used, the data foreach of said calibration points comprising distance data representing adistance between each said calibration point and the surveyinginstrument and the data for each of the images of each said calibrationpoint comprising image position data representing the position of theimage of each said calibration point on said image sensor andorientation data representing a horizontal angle of rotation of thetilting axis about the vertical axis and a vertical angle of tilting ofthe camera about the tilting axis and wherein on the basis of thedistance data for each of the calibration points and the image positionand orientation data for each of the images of the calibration pointsthe surveying instrument is calibrated simultaneously taking intoaccount at least one optical property of the camera and at least one ofthe relative orientation of the vertical axis and the tilting axis andthe orientation of the camera relative to one of the base element, thevertical axis and the tilting axis.

Further, according to a second aspect of the invention a method isprovided for calibrating a surveying instrument comprising a baseelement and a camera with an image sensor, the camera being rotatableabout a vertical axis fixed with respect to said base element and beingrotatable about a tilting axis, the tilting axis being rotated about thevertical axis with rotation of the camera about the vertical axis,wherein images of calibration points are generated at differentpositions on the image sensor and in two faces, wherein for each of saidcalibration points the distance data representing a distance between therespective calibration point and the surveying instrument and for eachimage of said calibration points position data representing the positionof the image of the calibration point on the image sensor, orientationdata representing a horizontal angle of rotation of the tilting axisabout the vertical axis and a vertical angle of tilting of the camera ofthe tilting axis are determined, and on the basis of the distance datafor each of the calibration points and the position and orientation datafor each of the images of the calibration points the surveyinginstrument is calibrated simultaneously taking into account at least oneoptical property of the camera and at least one of the relativeorientation of the vertical axis and the tilting axis and theorientation of the camera relative to one of the base element, thevertical axis and the tilting axis.

These methods according to the invention are suited for any surveyinginstrument equipped with a camera, in particular video-theodolites andvideo-tacheometers.

The surveying instrument comprises a base element, which is in a fixedposition relative to a point to be measured and in particular to theground when the instrument is in use. For example, the base element maybe mounted on a tripod or part of a tripod.

The surveying instrument further comprises a camera having an imagesensor. The camera may further comprise an optical system or at leastone lens to image points to be measured onto the image sensor.Preferably, the optical system may perform the complete imaging ofobject points at a distance from the surveying instrument. However, itis also possible that the camera only images an image of a calibrationpoint generated by other optics of the surveying instrument. Opticalproperties of the camera can be in particular the imaging properties ofthe camera. Optical properties can include properties of the optics ofthe camera such as focal length of the lens or objective of the camera,the position and orientation of the image sensor relative to the lens orobjective or image errors of the lens or objective of the camera.

The image sensor may be any at least two-dimensional arrangement ofphoto detecting elements which allows detecting light with a resolutionin the at least two dimensions. The arrangement of the photo detectingelements can be arbitrary. Preferably, the elements are arranged as anat least approximately rectangular matrix or in a honeycomb pattern. Theimage sensor may comprise in particular CMOS elements or CCD elements asphoto-detecting elements, in particular a CMOS array or a CCD array aswell known in the art. The surveying instrument may further comprise animage acquisition unit which is connected to the image sensor andgenerates images from signals provided by the image sensor. The imagesmay be provided in any suitable format as known to the person skilled inthe art. Preferably the image data obtained form the image sensor andrepresenting the image are compressed.

The camera is rotatable about a vertical axis of the surveyinginstrument which shall be in a vertical direction if the surveyinginstrument is used, but otherwise can have any direction. The camera canbe further tilted about a tilting axis which is rotated when the camerais rotated about the vertical axis. In particular, the camera may bemounted on an alidade rotatable about the vertical axis. The tiltingaxis is preferably orthogonal to the vertical axis except for possibletilting axis errors.

The surveying instrument may further comprise a so called horizontalcircle which serves to define the angular position of the tilting axiswith respect to a predetermined direction in a plane perpendicular tothe vertical axis, the vertical axis and thus the plane and thepredetermined direction being fixed with respect to the base element.Further, the surveying instrument may comprise a so called verticalcircle which can be used to determine the angular position of the camerawith respect to rotations about the tilting axis in a planeperpendicular to the tilting axis. The angular position may be definedwith any predetermined direction in the plane perpendicular to thetilting axis. Preferably the predetermined direction corresponds to thezenith when the instrument is in use or is coaxial with the verticalaxis. The horizontal angle and the vertical angle can be used touniquely define the orientation of the camera with respect to the baseelement.

The above-mentioned methods according to invention serve to calibratesuch a surveying instrument. Calibration may in particular mean, that arelationship is determined between a direction, in which an object pointlies with respect to a coordinate system fixed to the base element,termed the direction of the point, and the position of an image of theobject point on the image sensor as well as the measured horizontal andvertical angles used when capturing an image comprising the image of theobject point.

The method according to the second aspect differs from the methodaccording to the first aspect, in that the second method includes theacquisition of the data used for calibration. Thus, the method accordingto the first aspect may be performed using any data which may beprovided for example on a storage medium or via a connection to a devicefor carrying out the method.

For calibration at least two calibration points, which may also beregarded as or referred to as reference points, are used. Further, foreach calibration point at least one image, preferably several images ofthe calibration point on the image sensor are generated. To this end, ina fixed relative position of the calibration point and the surveyinginstrument, the camera may be rotated about the vertical axis and/ortilted about the tilting axis. The method according to the first aspect(and also according to the second aspect) uses data for each calibrationpoint representing a distance between the calibration points and thesurveying instrument and image position data and orientation data foreach image of each calibration point. The position data represent theposition of the image of the calibration point on the image sensor whenthe calibration point is imaged onto the image sensor by the optics ofthe surveying instrument being in an orientation defined by thecorresponding orientation data. The position data may for example begiven by an identification for a pixel in a CCD array at the location ofthe image of the calibration point. The orientation data in particularrepresent corresponding horizontal and vertical angles which may beobtained by use of suitable measuring devices such as the horizontal orvertical cycle or by setting the camera in the correspondingorientation.

The data are generated in two faces of the surveying instrument. It isnot necessary that two images of the same calibration point are obtainedby bringing the instrument from a first face into a second face. The useto two faces with surveying instruments such as theodolites ortacheometers is well known in the art. If an object point can be viewedin a first face of the camera, the same point can also be viewed, exceptin the case of too large axis errors etc., when the camera is rotated by200 gon or 180° and reversed by tilting about the tilting axis, i.e. inthe second face.

These data, in the following also termed calibration data, are used tocalibrate the surveying instruments. The calibration takes into accountat least the relative orientation of the tilting axis relative to thevertical axis, that is, in particular, a tilting axis error, andsimultaneously at least one optical property of the camera. An opticalproperty of the camera can be any property of the camera beingdetermined by the optics used for imaging and in particular the relativeposition between the optics and the image sensor.

Further, the calibration takes into account these error sources andproperties simultaneously, i.e. the calibration is not carried out in atleast two steps, in which a respective separate calibration is performedtaking into account either only one of the error sources or only oneoptical property of the camera.

Due to the use of data obtained in different faces of the surveyinginstrument and the simultaneous inclusion of potential axis errors aswell as an optical property of the camera a very precise and fastcalibration of the surveying instrument can be achieved. Further, onlyfew or no further instrument or camera data are necessary.

According to a third aspect of the invention a data processing system isprovided, the data processing system comprising a processor, a memory,in which there is stored a computer program for performing the methodaccording to the invention, when the program is executed by theprocessor, and further comprising an interface for reading dataassociated with calibration points and images of the calibration pointsused in the method. In particular the method according to the firstaspect of the invention may be carried out by the data processingsystem.

The data processing system may be a separate device which needs to beconnected to the surveying instrument only when the surveying instrumentshall be calibrated. However, the surveying instrument itself maycomprise a data processing system for processing of measured quantitiesaccording to predetermined tasks which has a memory in which thementioned computer program is stored. This processor may be also used torun the computer program. Depending on the type of data processingsystem the processor may be a special microprocessor, a processor asused in personal computers or workstations or a digital signalprocessor.

As an interface any means can be used which allow reading of the data.In the simplest case, it can be a keyboard for typing in the requireddata or a reading device for reading a data carrier which can beexchanged. The reading device may be e.g. a CD-ROM drive, a DVD-ROMdrive, a floppy disk drive or a reader for flash ROM memory devices,such as USB-sticks or memory cards. Advantageously, however, theinterface is suited for a data connection between the surveyinginstrument and the data processing system via cable or a wireless linksuch as bluetooth, wireless LAN or optical interfaces. In anotherembodiment, the interface is also suited for outputting commands to thesurveying instrument.

According to another aspect of the invention a computer program isprovided, the computer program comprising program code for performingthe method according to the first aspect of the invention, when thecomputer program is run on a computer.

According to a further aspect of the invention a computer programproduct is provided, the computer program product comprising programcode stored on a computer readable storage medium for performing themethod according to the first aspect of the invention, when said programproduct is run on a computer. The storage medium can be in particular amagnetic storage medium like a floppy disk or a hard disk, amagneto-optical disk or an optical storage medium like a CD or DVD.Also, permanent memories such as flash memory chips can be used.

The computer may be in particular realized by the data processing systemmentioned above.

In particular, the computer program or computer program product maycomprise program code for reading data associated with calibrationpoints and images of the calibration points on the image sensor, foreach of said calibration points the data comprising distance datarepresenting a distance between said calibration point and the surveyinginstrument and for each of the images of the calibration point the datacomprising image position data representing the position of the image ofthe calibration point on said image sensor and orientation datarepresenting a horizontal angle of rotation of the tilting axis aboutthe vertical axis and a vertical angle of tilting of the camera aboutthe tilting axis, and wherein on the basis of the distance data for eachof the calibration points and the image position and orientation datafor each of the images of the calibration points the surveyinginstrument is calibrated simultaneously taking into account at least oneoptical property of camera and at least one of the relative orientationof the vertical axis and the tilting axis and the orientation of thecamera relative to one of the base element, the vertical axis and thetilting axis. The data may be read from any storage medium or a memory,to which the data were written.

The calibration can be performed in several ways. According to apreferred embodiment of the invention, a model is used for calculatingthe positions of images of calibration points on the image sensor, themodel comprising adjustable model parameters and using distance data andorientation data associated with each of the images of the calibrationpoints, and for calibration the model is fitted to the position data byestimating at least directions of the calibration points and the modelparameters using the distance data, the position data and theorientation data. The direction of a calibration point is the directionin which the calibration point lies with respect to the instrument.Since the distance of the calibration points to the surveying instrumentis known, the directions of the calibration points suffice to fullydetermine the position of the calibration points with respect to thesurveying instrument, that is at least the base element. The directionsmay be represented by two angles of spherical coordinates of thecalibration points in a coordinate system fixed to the base element, thethird spherical coordinate being the distance between the calibrationpoint and the surveying instrument. This type of calibration allows toaccount for different properties of the instrument which may have aneffect on the position of an image of a calibration point on the imagesensor and also may allow the calculation of the quality of the fit. Thequality of the calibration strongly depends on the model used forcalibration. The better the model represent the properties of theinstrument, the better the model can be fitted to the calibration dataused for calibration.

The directions of the calibration points and the model parameters can beestimated by any suitable estimation method. However, it is preferredthat for estimation of the directions of the calibration points and ofthe model parameters a maximum likelihood estimate is used. Inparticular a least squares fit can be performed, which minimizesdeviations between the measured positions of the images of thecalibration points on the image sensor and positions of the images ofthe calibration points as calculated by the model. These types ofestimates can be carried out quite fast.

The imaging properties of a camera may depend on the distance of a pointto be imaged and/or the focusing state of the camera, e.g. the positionof the objective of the camera or at least one lens of the objective ofthe camera relative to the image sensor. To allow a precise calibrationalso in this case, it is preferred, that at least one of the modelparameters depends on the distance of the calibration point from thesurveying instrument or on a focusing state of the camera when capturingan image of the calibration point. The model parameter may depend in asmooth way on the distance or the focusing state of the camera.Alternatively, the range of possible distances or the range of objectiveand/or lens positions may be divided into a predetermined number ofsubranges. Then the parameter may take different values for eachsubrange.

In a particularly preferred embodiment, the model comprises atransformation for transforming coordinates of an instrument coordinatesystem fixed to the base element to a camera coordinate system fixed tothe camera and a camera model for mapping positions of calibrationpoints to positions on the image sensor in the camera coordinate system.The transformation has adjustable transformation parameters and thecamera model has adjustable camera parameters. For calibration, thecoordinates of the calibration points in the instrument coordinatesystem and the transformation parameters and camera parameters areestimated, so that positions of the images of the calibration points ascalculated by the model are fitted to the measured positions of imagesof the calibration points. This type of model allows a conceptuallyclear separation of characteristics of the instrument, in particular theinstrument axes and the mounting of the camera, from camera propertiesand in particular optical properties of the camera. By the methodaccording to this embodiment the magnitude of axis errors may bedetermined. These could be used to improve the construction of thesurveying instrument, its manufacture or a mechanical re-adjustment. Inparticular, at least one of the camera model parameters may depend onthe distance and/or focusing state of the camera as described in theparagraph above.

The transformation preferably includes at least one parameter relatingto a tilting axis error. Preferably, the calibration is performed alsotaking into account at least one of a vertical index error and acollimation error. In this context a collimation error is a deviation ofthe angle between the tilting axis and one of a camera axis, a sightingaxis, and an imaging axis provided by the camera model from a rightangle, i.e. 90° or 100 gon. The vertical index error is the deviation ofa reading of the vertical angle on a vertical circle when the camerapoints to the predetermined direction in plane perpendicular to thetilting axis, preferably the zenith, from the true vertical angle.Preferably, the transformation includes at least one parameterrepresenting one of the collimation error and the vertical index error.These errors can easily be accounted for when using a model comprising atransformation and a camera model, because the corresponding effects onthe transformation can be incorporated by suitable rotation matrices.

Further, the calibration preferably includes estimating the orientationof the camera relative to one of the tilting axis and an instrumentcoordinate system fixed to the base element. The orientation of thecamera may in particular relate to the orientation of an axis defined bymechanical elements of the camera such as an axis defined by lensholders. Preferably, in this case the transformation includes at leastone parameter representing the orientation of the camera relative to oneof the tilting axis and an instrument coordinate system fixed to thebase element. Hereby errors due to a mis-orientation of the camera maybe accounted for.

Generally, for the methods according to the invention, arbitrary cameramodels can be used. However, it is preferred, that the camera modelcomprises a projection center in which according to the camera model allrays from object points imaged onto the image sensor intersect, that inthe method at least one model parameter relates to the location of theprojection center. The location of the projection center may beexpressed relative to the base element, in particular to an instrumentcoordinate system fixed to base element. Especially in the case, whenthe field of view of the camera is rather limited preferably a pin holemodel may be used as a camera model which allows quite simple modelequations but still sufficient accuracy. To achieve a good accuracy ofthe calibration, the model preferably comprises at least three modelparameters which represent the location of the projection center. Thus,instruments having cameras in an arbitrary position relative to the axesof the instrument can be calibrated quite accurately.

Further, in order to represent some of the optical and in particularimaging properties of the camera, in one embodiment of the invention thecamera model comprises a parameter representing the distance between animage plane of the model and the projection center. In particular, theparameter may reflect the camera constant in the pinhole camera model.The image plane is preferably determined by the image sensor. To allow aprecise calibration also of cameras with a long focal length, at leastthe camera constant may depend on the distance and/or focusing state ofthe camera.

The location of the projection center relative to the image plane islargely determined by the optical properties of the optical system ofthe camera and thus represents an optical property of the camera in thesense of the invention. In particular, it may be related to the focallength of the optical system of the camera. Thus, different types ofoptical systems can be easily modeled without using further data on thecamera or the optical system of the camera.

To achieve a high accuracy of calibration, the camera model preferablycomprises model parameters representing distortions in the image. Thesedistortions may be due to e.g. imperfections of the optics of thecamera.

For determining model parameters relating to optical properties of thecamera, preferably the distance data associated with at least twocalibration points differ. Thus, the respective calibration points arelocated at different distances from the surveying instrument. Theaccuracy of the method and thus the accuracy of the calibration maybecome better, the larger the difference between the distances of thepoints from the surveying instrument is.

Further, in order to be able to determine model parameters representinga tilting axis error with good accuracy, preferably at least two imagesof at least one calibration point are used, which have a considerableheight, i.e. are close to the zenith.

Also, for obtaining a high accuracy of the calibration, preferably thenumber of images of calibration points is larger than the number ofadjustable model parameters, particularly much larger.

The accuracy of the calibration may be further enhanced, if for eachimage of at least one of the calibration points more than onedetermination of image position data and/or orientation data is made.

Preferably, the image position data comprise data explicitlyrepresenting the position on the image sensor. For instance, these datamay be the given by an identification code of a photo-detecting elementat the respective position. The identification code, e.g. the address ofa pixel or photo-detecting element, may be used to calculate a position,if necessary. However, the model can also provide the identificationcode directly.

In another embodiment, however, it is preferred that images captured bythe image sensor are obtained, the captured images comprising images ofat least one of the calibration points, and that the position of saidimages of said at least one of the calibration points on the imagesensor is determined by searching for the images of the calibrationpoint in the images. Thus, this embodiment allows to determine theactual positions of the images of a calibration point automatically froman image taken by the camera. The images of the calibration points canbe recognized in the image captured by the image sensor by any suitableknown object recognition methods.

For example, two images can be taken using the same orientation of thecamera, one image comprising the image of the calibration point and theother image showing the background only. Then, the images can besubtracted from each other so that only the calibration point remains asa signature in the resulting difference image, which signature can bedetected by means of a threshold criterion. If the shape of the targetrepresenting the calibration point is known, also templates can be used.The position of the template is varied to match the template to theimage of the calibration point in the image, which can be done forexample by correlation methods known in the art.

Thus, it is preferred that a template representing one of thecalibration points is used to search for the images of the calibrationpoint.

The distance data of the calibration points can be obtained by severalmethods. If the instrument is calibrated using predetermined calibrationpoints the distance of these points can be predetermined and eitherprovided as known data or included in a computer program speciallyadapted for use with these calibration points. To this end, apredetermined location can be provided in which the instrument is placedwhen it is calibrated. In particular, when a video-tacheometer iscalibrated using real calibration points, it is preferred, that thedistance of at least one of the calibration points to the surveyinginstrument is determined using opto-electronic distance metering.Opto-electronic distance metering, i.e. opto-electronic distancemeasurement, allows a quite precise measurement of distances. Further,the measurements can be made at the time when the images of thecalibration points are generated. For instance, two known methods may beused, for example determination of the distance by phase differences orby time-of-flight measurements using a pulsed laser beam.

As another alternative the calibration points can be provided in a knowndistance from the surveying instrument.

The calibration points may be provided in form of a real object, e.g. aco-operative target like a reflector (triple reflector) or an object inthe field. However, the calibration point does not need to be a point ofa real object. According to one preferred embodiment of the methodaccording to the second aspect of the invention, at least one objectpoint is imaged to a virtual calibration point which is imaged onto theimage sensor. The object point can be any real object or a point of areal object, for example a light source or an illuminated cross-hair orslit. This embodiment allows calibration also using calibration pointsin a large virtual distance from the surveying instrument.

In a particularly preferred embodiment of the method, the virtualcalibration points are generated by means of a collimator and a markthat can be shifted between a collimator objective, in particular ancollimator lens, and the focal point of the collimator objective.Generally more than one collimator can be used, in particular ifcalibration points at different heights shall be obtained. As anotheroption, in one collimator an arrangement of at least two marks can beused to generate a respective number of virtual calibration points atthe same time. Collimators are characterized in that they emit parallelrays of light and project a point at optical infinity to a finitedistance. The mark, e.g. a cross-hair, slit or a stop of other shape—isprovided at the collimator's focal point to generate an image of themark at infinity. The mark may be shiftable in the collimator by meansof a suitable drive mechanism, which can operated manually or by meansof a motor. Preferably, an extensible collimator is used, having anobjective part comprising an objective of the collimator and anillumination part comprising an illumination device, the objective partand the illumination part being shiftable with respect to each other.The mark may be mounted in the illumination part, so that shifting ofthe illumination part relative to the objective part may be used togenerate virtual images of the mark in different virtual distances.Preferably, the amount of shift can be read to micrometer accuracy.

Preferably the distance of a virtual calibration point is obtained onthe basis of the distance between an object point and imaging optics forgenerating the virtual image of the object point, the distance betweenthe imaging optics and the surveying instrument and on the basis of theimaging properties of the imaging optics. In particular in the case of acollimator, from the amount of shift relative to the focal point andfrom the focal length of the objective, one can determine the imagedistance of the virtual, erect image which represents the virtualcalibration point. This virtual image can be sighted at with thesurveying instrument to be calibrated. From the sum of the distance fromthe vertical axis of the instruments to the principle plane or principlefocal plane of the collimator objective or collimator lens and from theimage distance the final virtual distance between the instrument and thevirtual calibration point created by the collimator can be calculated.

A collimator can thus be used to generate the virtual calibration pointsat virtual distances as large as 2.000 meters or more whereas it isdifficult to create calibration points at such distances without acollimator. In particular, it may be difficult to find such a largedistance in a field that is free from sighting obstacles. Further,additional factors that can impair the calibration measurements at largedistances such as atmospheric phenomena like air turbulence can beavoided. Moreover, calibration point targets of different sizes would beneeded for different distances in order to obtain images ofapproximately equal size. Calibration by means of a collimator istherefore particularly suitable for calibration of instruments aftermanufacture as it takes little space and may work essentially automatic.Finally, this method makes a calibration independent of environmentalconditions, as the image sensor of a camera, for example detector matrixarray, which, as a rule, is composed of pixels, is frequently subject toinfluences by ambient light.

Preferably a data processing system according to the invention comprisesan output interface for outputting commands to a drive of a collimatorfor moving a mark of the collimator between an objective of thecollimator and the focal point of the collimator, and the computerprogram comprises instructions to move the mark to generate virtualcalibration points at different distances. In detail the instructionsmay generate control commands which are issued to the drive when theprogram is run. Preferably the computer program and computer programproduct according to the invention comprises program code may generatecontrol commands which are issued to a drive of a collimator having amark shiftable by the drive.

According to another aspect of the invention a system for calibrating asurveying instrument is provided, the surveying instrument comprising abase element and a camera with an image sensor, the camera beingrotatable about a vertical axis fixed with respect to said base elementand being rotatable about a tilting axis, the tilting axis being rotatedabout the vertical axis with rotation of the camera about the verticalaxis, the system comprising a collimator, a mark that can be shiftedbetween a collimator objective and a focal point of the collimatorobjective, and a drive for shifting the mark, and a data processingsystem according to claim 19 or to claim 19 and 20, the output interfacebeing connected with the drive of the collimator to move the mark inresponse to control commands generated by the data processing system.This system may used to perform the method according to the invention.Preferably, the drive comprises a stepping motor so that the position ofthe mark in the collimator can be set precisely. Alternatively, apositioning device can be used comprising a position sensor the signalsof which are used to control a motor of the drive to move the mark to apredetermined position.

The number of calibration points and the number of images of eachcalibration point may preferably be chosen according to the followingcriteria: The total number of images of all calibration points usedshall be larger than the number of model parameters used forcalibration. In order to obtain a good accuracy, the number of imagesshould be much larger than the number of parameters. As mentioned above,at least two calibration points should be provided in differentdistances from the surveying instrument.

In particular, to obtain a calibration also for off-axis points on theimage sensor it is preferred, that the images for at least one of thecalibration points are generated at different positions of the imagesensor. Preferably, they are distributed homogeneously over at least apredetermined area of the image sensor.

A predetermined distribution of image points can be obtained indifferent ways. According to a preferred embodiment of the invention,for at least one of the calibration points the positions of images ofthe image sensor are predetermined, the camera is directed to thecalibration point by at least one of rotating about the vertical axisand tilting about the tilting axis until the calibration point is imagedto the predetermined position of the image sensor, and the resultingorientation data are read and preferably stored. Preferably, the cameracan be re-oriented using a closed loop control. Preferably the dataprocessing system according to the invention further comprises aninterface for issuing control commands to the surveying instrument, thesurveying instrument comprising a base element and a camera with animage sensor, the camera being rotatable about a vertical axis fixedwith respect to said base element of the surveying instrument and beingrotatable about a tilting axis, the titling axis being rotated about thevertical axis with rotation of the camera about the vertical axis andthe surveying instrument comprising drives for rotating the camera aboutthe vertical axis and tilting the camera about the tilting axiscontrollable by the control commands, the computer program furthercomprising program code to generate images of a calibration point andpredetermined positions on the image sensor. Also the computer programand the computer program product according to the invention preferablycomprise a program code to generate images of a calibration point andpredetermined positions on the image sensor by issuing control commandsto the surveying instrument. The program code may be adapted to issuecontrol commands to be output over a suitable interface to the surveyinginstrument. The control commands may cause a re-orientation of thecamera by means of the drives. Once the re-orientation is completed,another image is captured and, e.g. sent to the data processing system,which determines the position of the image of the calibration point andits deviation from the predetermined position and issues further controlcommands. Thus, an automatic calibration is possible requiring only verylittle action by a person.

In one preferred embodiment of the method according to the second aspectof the invention for at least one of the calibration points images ofthe calibration point are generated in a regular arrangement on theimage sensor. In particular, in the case that an image sensor with arectangular arrangement of photo detecting elements is used, the regulararrangement may be given by a rectangular grid. The grid may chosen suchthat when positions are set that represent the angle combinations, thereference points are distributed as homogeneously as possible all overthe plane of the image sensor. Of course, other regular arrangements,for example hexagonal arrangements may be used.

If readings of the position data are taken always at the same positionson the image sensor, faults or defects in the image sensors may preventa reliable calibration. According to a preferred embodiment for at leastone of the calibration points an arrangement of cells covering apredetermined area of the image sensor is generated and random positionswithin the cells are used as positions of images of the calibrationpoint. Preferably the predetermined area of the image sensor comprisesat least the area of the image sensor used for surveying tasks. Thearrangement of cells may be generated by providing cell referencepoints, e.g. a geometrical center, at positions determined by thearrangement and the size and shape of the cells. Generally, the cellscan be arbitrarily arranged. Preferably, however, the cells areregularly arranged. For example a matrix like arrangement of cells canbe used. The random positions within the cells may be obtained by meansof a so called pseudo random-number generator which generatespseudo-random numbers distributed according to a predeterminedprobability distribution. Suitable random number generators are forexample discussed in Press, H. et al.: “Numerical Receipes in C”,Cambridge University Press, 1992, pp. 274-286. The use of randompositions allows reduction of the influence of faulty photo-detectionelements on the calibration.

In one preferred embodiment of the method at least two random positionsare given for each cell, and a first image of the calibration point isgenerated at the first of these random positions in the first face and asecond image of the calibration point is generated at the second of therandom positions in the second face. Thus, the random positions of eachangle combination need not be equal for the first and second faces andmay be determined separately. It is one advantage of this embodiment,that the random positions and the corresponding orientation data can bedetermined first for each cell in first face and later for each cell insecond face.

Alternatively, for at least one of the calibration points the camera isdirected into predetermined orientations, the orientations being definedby predetermined combinations of horizontal and vertical angles orhorizontal and vertical angle increments, and in each orientation imageposition data for a respective image of the calibration point areobtained. This embodiment allows a rapid setting of the horizontal andvertical angles, since no closed loop control is necessary to controlthe orientation of the camera. The rotations or tilts can be defined byangles to be reached or by angle increments between successivere-orientations of the camera. In particular, if a method according tothe invention is used for calibration of a large number of surveyinginstruments of the same type, the horizontal and vertical angles can bechosen such, that, apart from tolerances in the surveying instrument, adesired distribution of image positions on the image sensor can beobtained. These combinations of horizontal and vertical angles can bestored and used for each surveying instrument to be calibrated.

In a preferred embodiment for at least one of the images of calibrationpoints, the image position data and the corresponding orientation dataare obtained for both faces. Thus, after obtaining data for the firstface, the camera is rotated by 200 gon or 180 degrees about the verticalaxis and then tilted to a vertical angle of 400 gon minus the verticalangle set for the measurement in the first face. Herein it is assumedthat a vertical angle of 0 corresponds to the zenith. In this case atilting axis error may show up more explicitly in the data used forcalibration, so that calibration may be more precise and/or faster.

Once the calibration of a surveying instrument having a data processingunit for processing image data obtained by the image sensor iscompleted, the corresponding model data can be stored in data processingunit separate form the surveying instrument or a data processing unitintegrated into the surveying instrument. Further, a program may bestored in the data processing unit, which program allows computation ofdirections of object points imaged onto the image sensor on the basis ofthe model used for calibration, the obtained model parameters and theset horizontal and vertical angles.

Hence, according to a further aspect of the invention a surveyinginstrument is provided, the surveying instrument comprising a baseelement and a camera with an image sensor, the camera being rotatableabout a vertical axis fixed with respect to said base element and beingrotatable about a tilting axis, the tilting axis being rotated about thevertical axis with rotation of the camera about the vertical axis, thesurvey instrument being calibrated using a method according to theinvention. In particular, the surveying instrument may comprise anon-volatile memory in which values of the model parameters obtainedfrom calibration and program code for performing calculations using themodel used for calibration are stored, and a processor for executing theprogram.

Thus, according to another aspect of the invention also a surveyinginstrument is provided, the surveying instrument comprising a baseelement and a camera with an image sensor, the camera being rotatableabout a vertical axis fixed with respect to said base element and beingrotatable about a tilting axis, the tilting axis being rotated about thevertical axis with rotation of the camera about the vertical axis,wherein imaging of an object point on the image sensor by the camera canbe modeled by use of a camera model working a coordinate system fixed tothe camera and a transformation model for transforming coordinatesbetween an instrument coordinate system and the camera coordinatesystem, the instrument further comprising a data processing unit, inwhich program code is stored for determining a direction of an objectpoint captured by the camera using the camera and transformation models,wherein a direction from the origin of the instrument coordinate systemto the object point is calculated using a direction obtained by means ofthe camera model and the transformation model and the distance of theobject point from the origin of the instrument coordinate system.Preferably, the surveying instrument further comprises a distancemeasuring device for measuring the distance between an object point andthe origin of the instrument coordinate system. Preferably, the originof the instrument coordinate system is the intersection point or pointof closest approach of the tilting axis and the vertical axis, so thatthe instrument can be used as a known tacheometer with a telescope only.In particular, the camera may be offset from the origin of theinstrument coordinate system in a direction parallel to the tiltingaxis.

Also, a computer program for a surveying instrument is provided, thesurveying instrument comprising a data processing system, a base elementand a camera with an image sensor, the camera being rotatable about avertical axis fixed with respect to said base element and beingrotatable about a tilting axis, the tilting axis being rotated about thevertical axis with rotation of the camera about the vertical axis,wherein imaging of an object point on the image sensor by the camera canbe modeled by use of a camera model working in a coordinate system fixedto the camera and a transformation model for transforming coordinatesbetween an instrument coordinate system and the camera coordinatesystem, the computer program comprising program code for determining adirection of an object point captured by the camera using the camera andtransformation models, wherein a direction from the origin of theinstrument coordinate system to the object point is calculated using adirection obtained by means of the camera model and the transformationmodel and the distance of the object point from the origin of theinstrument coordinate system when the program is executed by the dataprocessing system.

According to yet another aspect of the invention a surveying instrumentis provided, the surveying instrument having a camera with an imagesensor, wherein imaging of an object point on the image sensor by thecamera can be modeled by use of a camera model having a projectioncenter, a display for displaying images based on images captured by theimage sensor, and a control unit for controlling the display to displaya mark indicating a sighting axis, the sighting axis being defined bythe projection center and the intersection point or point of closestapproach of the tilting axis and the vertical axis. This photogrammetricdefinition of the sighting axis has the advantage that a cross-hairdefined by the intersection of this photogrammetric sighting axis withthe image plane, i.e. the image sensor plane, the vertical index errorand the lateral collimation error are constant independent of distance.Theses errors can thus be easily taken into account in the processing ofmeasured data.

Exemplary embodiments of the invention are explained in more detailbelow by way of example and with reference to the drawings. In thedrawings

FIG. 1 shows a schematic perspective view of a tacheometer with acorresponding coordinate system and an object point;

FIG. 2A shows a top view of a tacheometer as in FIG. 1, the instrumenthaving a collimation error;

FIG. 2B shows a front view of a tacheometer as in FIG. 1, the instrumenthaving a tilting axis error;

FIG. 2C shows a side view of a tacheometer as in FIG. 1, the instrumenthaving a vertical height index error;

FIG. 3 shows a simplified perspective view of a video-tacheometer;

FIG. 4 shows a front view of a video-tacheometer for use with theinvention;

FIG. 5 shows a side view of a telescope unit of the video-tacheometer inFIG. 4;

FIG. 6 shows a schematic block diagram of the video-tacheometer in FIG.4;

FIG. 7 schematically shows the video-tacheometer in FIG. 4 with a dataprocessing system and an extensible collimator;

FIG. 8 shows a schematic sectional view of the collimator in FIG. 7;

FIG. 9 shows a diagram illustrating a pinhole camera model;

FIG. 10 shows a perspective diagram illustration coordinate systems andthe arrangement of axes and an image plane used in a model forcalibration in a method according to a first exemplary preferredembodiment of the invention;

FIG. 11 shows a top view of the arrangement in FIG. 10;

FIG. 12 shows a side view of the arrangement in FIG. 11;

FIG. 13 shows an overview of the method for calibration in form of aflow-diagram;

FIG. 14 shows a flow-diagram illustrating the generation of images ofcalibration points in section S1 of the method in FIG. 13;

FIG. 15 shows a more detailed flow-diagram illustrating the generationof images of a point in step S7 of the method shown in FIG. 14;

FIG. 16 shows a diagram illustrating the calculation of virtualdistances of virtual image points;

FIG. 17 shows a section of a first image sensor of the video-tacheometerin FIGS. 4 to 6 and an arrangement of cells covering the section of theimage sensor;

FIG. 18 show a setup for calibrating the video-tacheometer in FIGS. 4 to6 using a method according to a second preferred exemplary embodiment ofthe invention;

FIG. 19 shows a diagram for illustrating the calculation of directionswith respect to an instrument center;

FIG. 20 shows a schematic view of a display of the video-tacheometer inFIG. 1 and a mark indicating a photogrammetric sighting axis displayedon the display;

FIG. 21 shows a schematic diagram for explaining a method according toanother exemplary embodiment of the invention;

FIG. 22 shows a schematic sectional side view of a telescope unit ofanother video-tacheometer, which can be calibrated by the method inFIGS. 13 to 15;

FIG. 23 schematically shows the design of yet another tacheometer;

FIG. 24 is a perspective view of the two coordinate systems and themajor rotations;

FIG. 25 shows the essential relationships in a horizontal planecontaining a horizontal axis; and

FIG. 26 shows the essential relationships in a vertical plane containingthe vertical axis.

A video-tacheometer 11 which may be calibrated by means of a firstexemplary preferred embodiment of the method according to the inventionis shown in FIGS. 4 to 6 in a schematic and simplified manner.

An alidade 12 is arranged on a base element 13 of a tripod 14 serving asstand for the video-tacheometer 11. The alidade 12 is rotatable about avertical axis 15, which is oriented vertical to the ground if thevideo-tacheometer 11 is correctly oriented with respect to ground. Thealidade 12 carries a telescope unit 16 which comprises in a housing 17,a finder camera 18 having a wide field of view and a telecamera 19. Thetelescope unit 16 is rotatable about a tilting axis 20, which isorthogonal to the vertical axis 15 up to a tilting axis error. Thus, thetilting axis 14 rotates with rotation of one of the cameras 18 and 19about the vertical axis 12. A control panel 21 is removably mounted tothe alidade 12. The alidade 12 may be handled by means of a handle 86

Rotation and tilting drives 22 and 23, respectively, are provided forrotating the alidade 12 about the vertical axis 15 and for tilting thetelescope unit 16 about the tilting axis 20.

For measurement of an angle of rotation or of a horizontal angle aboutthe vertical axis 15, a graduated horizontal circle 24 for thehorizontal angle a sensing head 25 is provided. The horizontal circle 24is concentric with the vertical axis 15. The sensing head 25 is held onthe alidade 12 and can sense an angular position of the alidade 12 andthus of the telescope unit 16 and the cameras 18 and 19 relative to thebase element 13.

For measurement of an angle of rotation, i.e. tilt, about the tiltingaxis 20, i.e. of the vertical angle, a graduated vertical circle 26 forthe vertical angle is correspondingly mounted to the tilting axis 20being coaxial with the tilting axis 20. A sensing head 27 for thevertical angle which is also held on the alidade 12 can sense theangular position of the telescope unit 16.

The video-tacheometer 11 further comprises an optical plummet 28arranged in the alidade 12, which comprises a small telescope pointingdownwardly in a vertical direction. An optical axis of the smalltelescope substantially coaxially with the vertical axis 12. Thus, theoptical plummet 28 can be used to center or position thevideo-tacheometer 11 above a point on the ground, such as a boundarystone, for example. As an alternative an optical plummet could be usedwhich emits a light beam downwardly in a vertical direction, the lightbeam being substantially coaxial with the vertical axis 12.

An inclination sensor or clinometer 29 which is also arranged in thealidade 12 measures the inclination of the alidade 12 and, thus, of thevideo-tacheometer 11 in two directions which are orthogonal to eachother and, thus, allows to check whether the vertical axis 15 is in atrue vertical direction within a given accuracy of the measurement andwhether thus the tilting axis 20 is in a true horizontal directionrelative to the ground up to a tilting axis error.

Three optical devices are arranged in the telescope unit 16, which isshown from the front in FIG. 4 and in a lateral, sectional view in FIG.5. These are the finder camera 18, the telecamera 19 and adistance-measuring device 30.

The telecamera 19 comprises by an objective 31, a focusing lens 32 and afirst image sensor 33. An object or object point is imaged by theobjective 31 and a focusing lens 32 onto the image sensor 33, whereinfor focusing the image onto the image sensor the focusing lens 32 ismoved along the optical axis of the objective 31 and the focusing lens32, as indicated by the arrows in FIG. 5. The field of view of thetelecamera 19 is rather narrow and bounded by boundary rays 34 as shownin FIG. 5.

The finder camera 18 uses some of the optical elements of the telecamera19. The finder camera 18 comprises the objective 31, a beam splittingprism 35 arranged in the optical path of the objective 31, asupplementary objective 36, a diaphragm 37 and a second image sensor 38.The combined objective formed by the objective 31 and the supplementaryobjective 36 focuses light from a scene captured by the finder camera 18onto the second image sensor 38. In the combined objective, the lightpassing through the objective 31 is reflected by a semi reflectivesurface 39 of the beam splitting prism 35 towards the supplementaryobjective 36. The supplementary objective 36 reduces a focal length ofthe combined objective for the finder camera 18. The diaphragm 37ensures an essentially focused imaging onto the second image sensor 38for objects in a distance of more than a couple of meters, so that forthe finder camera 18 no focusing lens is necessary. Due to the reducedfocal length of the combined objective the field of view of the findercamera 18 (shown in FIG. 5 by the limiting rays 40) is larger than thatof the telecamera 19. Preferably, the range of view of the finder camera18 may be ten times the range of view of the telecamera 19 or more.

The first and second image sensors 33 and 38 are both CCD matrix sensorswhich comprise an arrangement of photo detecting elements which is to avery good approximation rectangular. Images captured by the imagesensors are processed by units discussed further below.

The distance measuring device 30 comprises an optical radiationemitting/receiving unit 41, a dichroic beam splitting prism 42 having abeam splitting layer 43 and the objective 31. The emitting/receivingunit 42 emits infrared radiation which is selectively reflected by thedichroic beam splitting layer 43 towards the objective 31. The infraredradiation may then hit a reflector or a target in the terrain from whereit is returned. The objective 31 focuses the returned infrared radiationto the emitting/receiving unit 41 via the beam splitting prism 42. Theemitting/receiving unit 41 emits pulses of infrared radiation andmeasures the time of flight of the pulses from the emitting/receivingunit 41 to the target and back to the emitting/receiving unit 41 anddetermines from the times of flight the distance of the target from thevideo-tacheometer 11.

Any movements of components of the video-tacheometer 11 are effectedelectronically. FIG. 6 shows a block diagram in which the variousfunctional blocks of the video-tacheometer 11 are schematically shown,including their connections to each other. The broken lines illustratethe physical units in which the respective components and devices arearranged.

A battery 44 which is arranged in the alidade 12 feeds a power supplyunit 45 which serves to supply the video-tacheometer 11 with power. Thepower supply unit 45 supplies all components and devices in the alidade12 and the telescope unit 6, as well as any modules connected to it,with the required operating voltages. For the sake of better overviewthese connecting lines are not shown. The individual components can beconnected individually via separate lines as the case for componentswithin the alidade 12 or by a central bus 46 which provides data andpower supply lines between the alidade 12 and the telescope unit 16.Slip rings 47 arranged on the tilting axis 20 connect the sections ofthe bus 46 in the alidade 12 and the telescope unit 16.

By these slip rings 47 electric or electronic components in thetelescope unit 16 can be supplied with power and can exchange data withcomponents in the alidade 12.

Slip rings 47′ arranged on the vertical axis 15 enable a power supplyfrom outside as well as a data transfer to or from external devices viaa plug, which is not shown.

For control or operation of the video-tacheometer 11, thevideo-tacheometer 11 is provided with the control panel 21 and operatingelements 48, 49 and 50 in the form of angle encoders arranged on thealidade 12 being operable by corresponding knobs. An important electricdevice for controlling operation of the video-tacheometer 11 is adevice-control unit 51 arranged in the alidade 12 and provided withpower by the power supply unit 45.

The control panel 21 serves for communication between the operator andthe video-tacheometer and is provided with a keyboard 52 for input, adisplay 53 for output of data and images captured by one of cameras 18or 19, respectively, e.g. an LCD, and a computer 54 which is connectedto the display 53 and the keyboard 52.

The control panel 21 is connected to the device-control unit 51 arrangedin the alidade 12 and the power supply unit 45 via a releasableconnection 55. Since the control panel 21 is removable, it may beequipped with its own battery, which ensures that the computer 54continues to work even when the control panel 21 is removed from thealidade 12. The computer 54 is connected to the device-control computer51 via a connection 56 and can perform numerous geodesic calculations bymeans of its program and data memories.

The operating elements 48, 49 and 50 are connected to the device-controlcomputer 51 via a corresponding interface 57. This interface 57 allowsto generate signals corresponding to a rotary position of the operatingelements 48, 49 and 50, respectively, which are transmitted to thedevice-control unit 51.

The operating elements 48 and 49 serve for controlling rotation of thealidade 12 about the vertical axis 15 and tilting of the telescope unit16 about the tilting axis 20, respectively. In response to signals fromthe operating elements 48 and 49, respectively, and the interface 57 thedevice-control unit 51 controls via control circuits 58 and 59 in thealidade 12 the drives 22 and 23 to rotate the alidade 12 about thevertical axis 15 and to tilt the telescope unit 16 about the tiltingaxis 20, respectively. Angle measurements may be used to control thedrives 22 and 23.

Drives 22 and 23 do not need to be controlled solely by the operatingelements 48 and 49, respectively, but can also be controlled on thebasis of a program stored and executed in the device-control unit 51 oron the basis of commands sent to the device-control unit 51.

The drives 22 and 23 cooperate with the angle-measuring devices, i.e.the graduated horizontal circle 24 for the horizontal angle and thecorresponding sensing head 25, or the graduated vertical circle 26 forthe vertical angle and the corresponding sensing head 27, respectively,such that the alidade 12 with the telescope unit 16 can be rotated asdesired about the vertical axis 15 and the telescope unit 16 can berotated about the tilting axis 20 in a measurable manner and can bebrought in to a desired horizontal and vertical angle position. Thispurpose is served inter alia, by the device-control computer 51, whichreceives signals from the sensing heads 25 and 27 and controls thecontrol circuit 58 for the horizontal drive 22 and the control circuit58 for the vertical drive 23 in response to said signals.

The angles which the alidade 12 is to be rotated to about the verticalaxis 5 and which the telescope unit 16 is to be rotated to about thetilting axis 20 can be provided in three ways. First, the operatingelements 48 and 49 allow input of corresponding angles to thedevice-control computer 51. Second, the device-control computer 51 candetermine the angle to be set also as a function of data from othercomponents of the video-tacheometer 11 and can accordingly control thecontrol circuits 58 and 59, respectively. Third, corresponding data canbe input to the control-device unit 51 via an interface 60, for examplea RS232-interface.

A radio module 61, which is connected to the device-control computer 51and has an antenna 62, serves to exchange data with remote devices, suchas a remote control. For example, the video-tacheometer 11 can beremote-controlled by a remote control or station, which is located atthe target point of the measurement, but it is not shown in the Figures.

For processing the signals of the image sensors 33 and 38, a datacompression unit 63 is provided in the telescope unit 16 whichcompresses image data received from the image sensors 33 and 38. Thecompressed data can then be sent to the device-control unit 51 which mayprocess and/or forward the data to the computer 54 and the display 53.

For controlling the position of the focusing lens 32 the operatingelement 50 of the same type as the operating elements 48 and 49 arrangedat the alidade 12 provides signals via the interface 57 to thedevice-control unit 51 which in turn provides corresponding controlsignals to a servo control unit 64 arranged in the telescope unit 16 todrive a corresponding focusing drive for shifting the focusing lens 32.This drive is not shown in the Figures.

The device-control unit 51 is further connected to the above-mentionedoptical plummet 28 and the inclination sensor 29.

The device-control unit 51 comprises a volatile memory, a non-volatilememory and a processor for executing a program stored in thenon-volatile memory. The program is suited to process images obtainedfrom the image sensors 33 and 38, respectively, and display the processimages on the display 53 using the computer 54 of the control panel 21.The program comprises further a program module, which can calculate adirection of an object point an image of which was captured by thetelecamera 19 as function of the position of the image of the objectpoint on the image sensor 33 and the horizontal and vertical angles readfrom the horizontal and vertical circles 24 and 26. The object point maybe selected by a pointing device such as a mouse, not shown in theFigures and connected to the device-control unit 51 via the computer 54.

The video-tacheometer 11 may be calibrated by means of a method forcalibrating a surveying instrument according to an first exemplaryembodiment of the invention using a data processing system 65 accordingto an first exemplary embodiment of the invention and an extensiblecollimator 66.

The setup is schematically shown in FIG. 7.

The data processing system 65 comprises a processor 67, a memory 68 forstoring a program to be executed by the processor 67 and permanent andtemporary data and an interface 69 for reading data used for calibrationand sending commands to the surveying instrument to be calibrated, i.e.the video-theodolite 11. In the present embodiment, interface 69 is anRS232 interface. The data processing system 65 further comprises areader for a storage medium, in this case a CD-ROM drive 70, to read acomputer program according to a first preferred exemplary embodiment ofthe invention from a storage medium in the form of a CD 71 on which thecomputer program according to the first preferred exemplary embodimentof the invention is stored. When the computer program is read from theCD 71 by means of the CD-ROM drive 70 and stored in the memory 68 it canbe executed by the processor 67 to perform the steps of the calibrationmethod to be executed by a data processing system.

The data processing system 65 is connected to the interface 60 of thevideo-tachometer 11 via a connection 72, in this example a suitablecable.

The set up further contains the collimator 66 which serves to generatevirtual calibration points. The collimator 66 which is shown in moredetail in FIG. 8 comprises guiding tube element 73 and guided tubeelement 74. The guided tube element 74 is slidable in the guiding tubeelement 73 while being guided by the tube element 73.

The guiding tube element 73 may be mounted in a fixed position relativeto the ground by mounting means not shown in the Figures. The guidedtube element 74 may be slid relative to the guiding tube element 73 bymeans of a rack-and-pinion drive 75 to be operated by a knob not shownin FIG. 8. The position of the guided tube element 74 relative to theguiding tube element 73 may be determined by suitable measuring devicesup to micrometer accuracy, e.g. by means of scales 87 engraved in thetube elements 73 and 74.

An illumination device 76 arranged in the guided tube element 74illuminates a ground glass screen 77. The illuminated ground glassscreen 77 illuminates a first cross-hair 78. A beam splitter 79 arrangedin the light path of the light emitted by illumination device 76redirects light having passed the first cross hair 78 towards anobjective 80 mounted in the guiding tube element 73. The objective 80images the cross-hair 78 as real or virtual image to a distancedetermined by the distance between the objective 80 and the firstcross-hair 78. For calibration purposes, the first cross-hair 78 ispositioned between the objective 80 and its object side focal point. Thecross-hair 78 thus represents a floating mark which can be used togenerate virtual calibration points.

A second cross-hair 81 is arranged on the optical axis of the objective80 past the beam splitter 79 and may be viewed by an eyepiece 82.

For calibration of the video-tacheometer 11 with the telecamera 19 beingactive, a model is used which includes model parameters to be adjustedfor calibration. The model comprises two submodels.

The first submodel is a model for a transformation of coordinates in acoordinate system fixed to the base element 13 to a camera coordinatesystem fixed to the camera, that is telecamera 19, including asparameters the horizontal and vertical angles set at the instrument andparameters relating to axis errors as mentioned in the introduction,that is a tilting axis error and some form of collimator error andvertical index error.

The second submodel is a camera model which represents the imaging of anobject point by the camera onto the image sensor of the camera. In thisembodiment, a pin hole model is used.

In the model, essentially two coordinate systems are used. The firstcoordinate system, termed instrument coordinate system, is fixed withrespect to the base element 13 (see FIG. 4). It is a Cartesiancoordinate system with the origin at the intersection of the verticalaxis 15 and the tilting axis 20 and with the X axis, the Y axis and theZ axis being orthogonal to each other. In the case that these axes donot intersect, the point of closest approach of these axis is used asthe origin of the coordinate system. The X axis and Y axis areorthogonal to the vertical axis 15 and thus horizontal, if the verticalaxis 15 is perpendicular to the ground. In this coordinate system apoint P has Cartesian coordinates (X, Y, Z).

Second, a camera coordinate system is used, which is fixed with respectto the camera 19. It is defined by an x-axis, a y-axis and a z-axis, allthree axis being orthogonal to each other. The position of a point P canbe described by the coordinates (x, y, z) in the camera coordinatesystem.

In the following, coordinates in the instrument coordinate system arealways denoted by capital letters whereas coordinates in the cameracoordinate system are always denoted by small letters.

First, the camera model is described in more detail with reference toFIG. 9.

The pinhole model used as a camera model assumes that a point P imagedby the camera onto the image sensor may be described by a projection ofthis point via a projection center O onto an image plane IP which isrelated to the image sensor 33 and may in particular be in the sameplane.

Thus, the pinhole model is determined by the image plane IP and theposition of the projection center O relative to the image plane. Sincethe position of the projection center relative to the projection centeris determined by the camera optics, here the objective 31 and thefocusing lens 32, the position represents optical properties of thecamera and in particular imaging properties of the camera. Imaging of anobject point P to the image plane is represented by a projection of theobject point through the projection center O onto the image plane (seeFIG. 9). The image plane is assumed to be essentially the plane of theimage sensor so that the x axis and y axis of the camera coordinatesystem are parallel to the image plane. The z-axis of the rectangularcamera coordinate system is the line through the projection centerorthogonal to the image plane. Since the image is always in the imageplane the position can be characterized solely by the x and ycoordinates.

Let (x,y,z) be the coordinates of the point P in the camera coordinatesystem and (x₀, y₀, z₀) the projection center coordinates in the cameracoordinate system. Thus, the piercing point H_(p) of the line orthogonalto the image plane IP through the projection center O, i.e. the z-axis,has coordinates x₀ and y₀ in the x-y-plane. Further, (x′, y′, z′) denotethe coordinates of the image P′ of the point P generated by the camerain the image plane. If the camera optics do not create distortions, oneobtains the following relationship by simple geometric arguments (seeFIG. 9):

$\frac{x^{\prime} - x_{0}}{c_{k}} = \frac{x - x_{0}}{z - z_{0}}$$\frac{y^{\prime} - y_{0}}{c_{k}} = {\frac{y - y_{0}}{z - z_{0}}.}$

Herein c_(k) is the so-called camera constant representing the distancebetween the projection center and the image plane. Thus, z′=c_(k) holdstrue.

The camera optics may create distortions in images, the distortionsbeing caused to imperfections of the lenses used in the camera opticsand/or their alignment. To account for first-order radial distortionsanother parameter v is introduced. A relative change in position of theimage caused by a distortion is modeled as a constant v times the squareof the radial distance of the image from the piercing point H_(P). Ifthe image of a point (x, y, z) falls at (x′, y′) in the image planewithout the distortion the squared radial distance of the image pointfrom the piercing point H_(P) is (x′−x₀)²+(y′−y₀)². Thus, distortioncorrections Δx′ and Δy′ are added (see FIG. 9) which results in theequations:

$x^{\prime} = {x_{0} + {c_{k}\frac{x - x_{0}}{z - z_{0}}} + \; {\Delta \; x^{\prime}}}$$y^{\prime} = {y_{0} + {c_{k}\frac{y - y_{0}}{z - z_{0}}} + {\Delta \; y^{\prime}}}$

with

Δx′=v((x′−x ₀)²+(Y′−y ₀)²)(x′−x ₀)

Δy′=v((x′−x ₀)²+(y′−y ₀)²)(y′−y ₀)

and v being a camera model parameter representing the above-mentionedfirst-order radial distortions of the optics of the camera.

These equations are valid only in the camera coordinate system. If thecoordinates of the object point shall be expressed in the instrumentcoordinate system, a transformation between these coordinate systems innecessary. This is the submodel for transformation.

Generally, the transformation can be expressed by a sequence of threerotations about the coordinate system axis and a translation vector inspace. Thus coordinates p^(t)=(x, y, z) of a point P in the cameracoordinate system are transformed into coordinates P^(t)=(X, Y, Z) inthe instrument coordinate system by the equation:

p=T+R ⁻¹ P

wherein T is a translation vector and R⁻¹ is the inverse of a product Rof rotation matrices. Since during calibration the position of theprojection center and the position and orientation of the image planeare adjusted the origin of the camera coordinate system can be chosen tobe the projection center, resulting in the equation:

p=R ⁻¹(P−O)

Inserting this relationship into the equations for x′ and y′ yields theso called collinearity equations:

$x^{\prime} = {x_{0}^{\prime} - {c_{K}\frac{{r_{11}\left( {X - X_{0}} \right)} + {r_{21}\left( {Y - Y_{0}} \right)} + {r_{31}\left( {Z - Z_{0}} \right)}}{{r_{13}\left( {X - X_{0}} \right)} + {r_{23}\left( {Y - Y_{0}} \right)} + {r_{33}\left( {Z - Z_{0}} \right)}}} + {\Delta \; x^{\prime}}}$$y^{\prime} = {y_{0}^{\prime} - {c_{K}\frac{{r_{12}\left( {X - X_{0}} \right)} + {r_{22}\left( {Y - Y_{0}} \right)} + {r_{32}\left( {Z - Z_{0}} \right)}}{{r_{13}\left( {X - X_{0}} \right)} + {r_{23}\left( {Y - Y_{0}} \right)} + {r_{33}\left( {Z - Z_{0}} \right)}}} + {\Delta \; y^{\prime}}}$

with

Δx′=v((r ₁₁(X−X ₀)+r ₂₁(Y−Y ₀)+r ₃₁(Z−Z ₀))²+(r ₁₂(X−X ₀)+r ₂₂(Y−Y ₀)+r₃₂(Z−Z ₀))²)(r ₁₁(X−X ₀)+r ₂₁(Y−Y ₀)+r ₃₁(Z−Z ₀))

Δy′=v((r ₁₁(X−X ₀)+r ₂₁(Y−Y ₀)+r ₃₁(Z−Z ₀))²+(r ₁₂(X−X ₀)+r ₂₂(Y−Y ₀)+r₃₂(Z−Z ₀))²)(r ₁₂(X−X ₀)+r ₂₂(Y−Y ₀)r ₃₂(Z−Z ₀))

wherein r_(ij), i,j=1, . . . , 3 are the matrix elements of R and thecoordinates of the projection center O in the instrument coordinatesystem are (X₀, V₀, Z₀).

Since the origin of the camera coordinate system is chosen to be theprojection center and the z axis is assumed to be orthogonal to theimage plane, an image position (x″, y″) read on the image sensor in aimage sensor coordinate system having a x″ axis and a y″ axis beingdirected along rows and columns of the matrix of the CCD sensorcorresponds to an image position in the camera coordinate system givenby x′=x″−x_(s)″ and y′=y″−y_(s)″, with (x_(s)″, y_(s)″) being thecoordinates of the position of the intersection of the z axis with theimage plane as measured by the image sensor, i.e. the position of thecorresponding pixel on the image sensor. Thus, in the above mentionedequations x′ and y′ are replaced by x″−x_(s) and y″−y_(s).

In summary, the parameters of the camera model are the coordinatesx_(s), y_(s) of the piercing point, the camera constant c_(k) and theparameter v representing the distortion properties of the camera optics.Due to the definition of the camera coordinate system x₀=y₀=0 holdstrue.

The transformation between the camera coordinate system and theinstrument coordinate system can be derived in various ways, for exampleby performing successive rotations of the camera coordinate systemstarting from an orientation in which it coincides with the instrumentcoordinate system as set out below.

FIG. 10 shows the camera coordinate system with coordinate axis x, y andz, the image coordinate system with coordinates x″, y″ and an originwith the coordinates (x_(s)″, y_(s)″, c_(k)), the x″- and the y″−axisbeing parallel to the x- and y-axis, and their relation to theinstrument coordinate system (X,Y,Z). In FIG. 10, the origin of theinstrument coordinate system lies at the intersection of the theoreticaltilting, vertical and sighting axes (i.e. in the instrument center ortacheometer center, respectively). For these theoretical axes theabove-mentioned conditions are satisfied: The theoretical vertical axis15 is assumed to be perpendicular to the ground, the angle between thetheoretical tilting axis 20′ and the theoretical vertical axis 15 andthe angle between the theoretical sighting axis 83 and the theoreticaltilting axis 20′ are assumed to be right angles. All three axesintersect in one point which is the origin of the instrument coordinatesystem. It is further assumed that the actual vertical axis is thetheoretical vertical axis. The Z axis of the instrument coordinatesystem coincides with the vertical axis of the instrument, and the Yaxis coincides with the zero direction marked on the horizontal circle24.

The origin of the camera coordinate system is the projection center O.However, in FIG. 10, for the sake of a better overview, the origin isshown shifted to the image plane. The principal point H_(P), i.e. thepiercing point of the line through the projection center and orthogonalto the image plane IP, has the coordinates x_(s)″ and y_(s)″ in theimage coordinate system in the image plane.

As shown in FIGS. 10 to 12, the actual tilting axis 20 may deviate fromthe theoretical tilting axis 20′ by an angle i, which is the deviationof the angle between the actual tilting axis 20 and the vertical axis 15from a right angle. Thus, the angle i represents a tilting axis error.

Furthermore, the theoretical sighting axis 83 does not need to runthrough the projection center O. This deviation may be expressed by twoangles c₀ and z₀. The angle c₀ is defined in a plane given by thetheoretical tilting axis 20′ and the theoretical sighting axis 83 as theangle between the theoretical tilting axis 20′ and the line through theprojection center O and the intersection point of the theoreticalsighting axis 83 and the theoretical tilting axis 20′. The angle z₀ isdefined in a plane given by the vertical axis 15 and the theoreticalsighting axis 83 as the angle between the theoretical sighting axis 83and the line through the projection center O and the intersection pointof the theoretical sighting axis 83 and the theoretical tilting axis20′.

A deviation of an telescope axis 110, the telescope axis 110 beingdefined by the lens mounting of the camera lenses, from the theoreticalsighting axis 83 is defined by an angle c_(F) between the telescope axis110 and the theoretical sighting axis 83.

The camera coordinate system may also be rotated about the axis of theinstrument coordinate system by angles ω, φ, κ which are assumed to beindependent of any errors and directions of the video-tacheometer 11.

The above mentioned deviations cause deviations of the actual or truehorizontal and vertical angles from the respective angles as read fromthe horizontal and vertical circle 24 and 26, respectively.

The actual or effective angle of tilting of the camera coordinate systemis given by

V ₀ =V _(m) +Z ₀

as can be determined from FIGS. 10 and 12. Therein V_(m), denotes thevertical angle as read from the vertical circle 26.

The angles c₀ and c_(F) have the same influence on the sphericalcoordinates of the projection center and actual horizontal angle,respectively, as a collimation error:

$\frac{c_{0}}{\sin \left( V_{0} \right)}\mspace{14mu} {and}\mspace{14mu} {\frac{c_{F}}{\sin \left( V_{0} \right)}.}$

The angle i causes a deviation in the horizontal angle of

i cot(V₀).

The effective horizontal angle Hz_(eff), by which the camera coordinatesystem is rotated about the vertical axis thus reads:

${H\; z_{eff}} = {{H\; z_{m}} + \frac{c_{F}}{\sin \left( V_{0} \right)} + {i \cdot {\cot \left( V_{0} \right)}}}$

wherein Hz_(m) denotes the horizontal angles as read from the horizontalcircle 24.

A detailed derivation of these formulas can be found in Deumlich, F.,Staiger, R.: “Instrumentenkunde der Vermessungstechnik”, Heidelberg,Germany, 9. edition, pages 206 to 208.

The rotation matrix R⁻¹ can be obtained by considering the followingsequence of rotations of the camera coordinate system starting in anorientation in which it coincides with the instrument coordinate system.

First, the camera coordinate system is rotated about the vertical axisby the effective horizontal angle Hz_(eff). The correspondingcoordinates in the rotated coordinate system may be obtained by therotation matrix

${R_{\kappa}^{- 1}\left( {H\; z_{eff}} \right)} = {\begin{bmatrix}{\cos \left( {{- H}\; z_{eff}} \right)} & {\sin \left( {{- H}\; z_{{eff}\;}} \right)} & 0 \\{- {\sin \left( {{- H}\; z_{eff}} \right)}} & {\cos \left( {{- H}\; z_{eff}} \right)} & 0 \\0 & 0 & 1\end{bmatrix}.}$

The tilting axis error is accounted for by a rotation about the y-axisof the transformed, i.e. rotated, camera coordinate system by the anglei.

The corresponding coordinate transformation is given by the rotationmatrix

${R_{\varphi}^{- 1}(i)} = \begin{bmatrix}{\cos (i)} & 0 & {\sin (i)} \\0 & 1 & 0 \\{- {\sin (i)}} & 0 & {\cos (i)}\end{bmatrix}$

Now, the camera coordinate system rotated twice is further rotated aboutthe x-axis of the twice rotated camera coordinate system by theeffective vertical angle V₀. Taking into account that in geodesy thevertical angle is measured from the zenith the corresponding rotationmatrix for the coordinate transformation reads:

${R_{\omega}^{- 1}\left( V_{0} \right)} = \begin{bmatrix}1 & 0 & 0 \\0 & {\cos \left( {{200\; {gon}} - V_{0}} \right)} & {- {\sin \left( {{200\; {gon}} - V_{0}} \right)}} \\0 & {\sin \left( {{200\; {gon}} - V_{0}} \right)} & {\cos \left( {{200\; {gon}} - V_{0}} \right)}\end{bmatrix}$

In a fourth step, the camera coordinate system as rotated so far isrotated further by the angle c_(F) about the current y axis. Thecorresponding coordinate transformation can be written in terms of therotation matrix

${R_{\varphi}^{- 1}\left( c_{F} \right)} = {\begin{bmatrix}{\cos \left( c_{F} \right)} & 0 & {\sin \left( c_{F} \right)} \\0 & 1 & 0 \\{- {\sin \left( c_{F} \right)}} & 0 & {\cos \left( c_{F} \right)}\end{bmatrix}.}$

Finally, the camera coordinate system obtain by the last rotation isrotated about the x axis by an angle ω, about the y axis by an angle φand about the z axis by an angle κ. The corresponding rotation matrixreads

$\left( {{R_{\omega}(\omega)} \cdot {R_{\varphi}(\varphi)} \cdot {R_{\kappa}(\kappa)}} \right)^{- 1} = \begin{bmatrix}{{\cos (\varphi)}{\cos (\kappa)}} & {{- {\cos (\varphi)}}{\sin (\kappa)}} & {\sin (\varphi)} \\\begin{matrix}{{\cos (\omega){\sin (\kappa)}} +} \\{\sin (\omega){\sin (\varphi)}{\cos (\kappa)}}\end{matrix} & \begin{matrix}{{\cos (\omega){\cos (\kappa)}} -} \\{\sin (\omega){\sin (\varphi)}{\sin (\kappa)}}\end{matrix} & {{- {\sin (\omega)}}{\cos (\varphi)}} \\\begin{matrix}{{\sin (\omega){\sin (\kappa)}} -} \\{\cos (\omega){\sin (\varphi)}{\cos (\kappa)}}\end{matrix} & \begin{matrix}{{\sin (\omega){\cos (\kappa)}} +} \\{\cos (\omega){\sin (\varphi)}{\sin (\kappa)}}\end{matrix} & {{\cos (\omega)}{\cos (\varphi)}}\end{bmatrix}$

The complete rotation matrix having matrix elements r_(ij), i,j=1, . . ., 3 thus reads

R=R _(κ)(Hz _(K))·R _(φ)(k ₀)·R _(ω)(V ₀)·R _(φ)(c _(F))·R _(ω)(ω)·R_(φ)(φ)·R _(κ)(κ).

From FIG. 10, the coordinates of the projection center O in theinstrument coordinate system can be written as

$O = {\begin{bmatrix}X_{0} \\Y_{0} \\Z_{0}\end{bmatrix} = \begin{bmatrix}{S_{0} \cdot {\sin \left( {V_{m} + z_{0}} \right)} \cdot {\sin \begin{pmatrix}{{H\; z_{m}} + \frac{c_{0}}{\sin \left( {V_{m} + z_{0}} \right)} +} \\{i \cdot {\cot \left( {V_{m} + z_{0}} \right)}}\end{pmatrix}}} \\{S_{0} \cdot {\sin \left( {V_{m} + z_{0}} \right)} \cdot {\cos \begin{pmatrix}{{H\; z_{m}} + \frac{c_{0}}{\sin \left( {V_{m} + z_{0}} \right)} +} \\{i \cdot {\cot \left( {V_{m} + z_{0}} \right)}}\end{pmatrix}}} \\{S_{0} \cdot {\cos \left( {V_{m} + z_{0}} \right)}}\end{bmatrix}}$

wherein S₀ denotes the distance of the projection center from the originof the instrument coordinate system.

Thus, the complete transformation is given by the rotation matrix R andthe position of the projection center. The transformation parametersused in the transformation, i.e. the transformation parametersparameterizing the transformation, are i, c₀, c_(F), z₀, S₀, ω, φ and κ.The transformation also depends on the horizontal and vertical anglesHz_(m) and V_(m) as read on the horizontal circle.

Using the collinearity equations and the coordinate transformation it ispossible to calculate the positions x″ and y″ of an image of an objectpoint which has spherical coordinates Hz, V and S and thus Cartesiancoordinates (S cos(Hz) sin(V), S sin(Hz) sin(V), S cos(V)) in theinstrument coordinate system and which is imaged at horizontal andvertical angles Hz_(m) and V_(m) using the camera model parameters andthe transformation parameters:

$x^{''} = {x_{s}^{\prime} - {c_{K}\frac{{r_{11}\left( {X - X_{0}} \right)} + {r_{21}\left( {Y - Y_{0}} \right)} + {r_{31}\left( {Z - Z_{0}} \right)}}{{r_{13}\left( {X - X_{0}} \right)} + {r_{23}\left( {Y - Y_{0}} \right)} + {r_{33}\left( {Z - Z_{0}} \right)}}} + {\Delta \; x^{\prime}}}$$y^{''} = {y_{s}^{\prime} - {c_{K}\frac{{r_{12}\left( {X - X_{0}} \right)} + {r_{22}\left( {Y - Y_{0}} \right)} + {r_{32}\left( {Z - Z_{0}} \right)}}{{r_{13}\left( {X - X_{0}} \right)} + {r_{23}\left( {Y - Y_{0}} \right)} + {r_{33}\left( {Z - Z_{0}} \right)}}} + {\Delta \; y^{\prime}}}$

with

Δx′=v((r ₁₁(X−X ₀)+r ₂₁(Y−Y ₀)+r ₃₁(Z−Z ₀))²)+(r ₁₂((X−X ₀)+r ₂₂(Y−Y₀)+r ₃₂(Z−Z ₀))²)r₁₁(X−X ₀)+r ₂₁(Y−Y ₀)+r ₃₁(Z−Z ₀))

Δy′=v((r ₁₁(X−X ₀)+r ₂₁(Y−Y ₀)+r ₃₁(Z−Z ₀))²+(r ₁₂(X−X ₀)+r ₂₂(Y−Y ₀)+r₃₂(Z−Z ₀))²)(r ₁₂(X−X ₀)+r ₂₂(Y−Y ₀)+r ₃₂(Z−Z ₀))

The above equations can be written for brevity, as

x″=U _(x)(i,c ₀ ,c _(F) ,z ₀ ,ω,φ,κ;S ₀ ,c _(K) ,x _(s) ,y _(s) ,v;S,V_(m) ,Hz _(m)) and

y″=U _(y)(i,c ₀ ,c _(F) ,z ₀ ,ω,φ,κ;S ₀ ,c _(K) ,x _(s) ,y _(s) ,v;S,V_(m) ,Hz _(m)).

The method according to the first preferred embodiment of the inventionis described with reference to FIGS. 13 to 15.

The method may be subdivided into four major sections.

In the first section S1, calibration data are obtained by means of thecollimator 66, the data processing system 65 and the video-tacheometer11.

By means of the collimator 66 several virtual calibration points P_(i),i=1, . . . , N, N being a positive integer number, are provided.Distance data for these virtual calibration points are obtained bymeasuring the distance between the cross-hair 78 and the objective 80along the light path and the distance between the objective lens 80 andthe video-tacheometer 11. Further, for each calibration point images ofthe calibration point are generated in different positions and the imagesensor and corresponding image position data representing the positionof the images on the image sensor as well as orientation datarepresenting corresponding horizontal and vertical angles are obtainedin both faces of the video-tacheometer 11. Some of the steps are carriedout by means of the computer program in the data processing system 65

In a second section S2, a model is provided which is used forcalibration, which in this example is the above-mentioned model. Themodel is provided in the form of program code of the computer programexecuted in the data processing system 65.

In a third section S3, values for the model parameters and datarepresenting directions associated with the calibration points in theinstrument coordinate system are estimated using a least squaresestimate method. All steps in this section are also performed by meansof the computer program in the data processing system 65.

In a fourth section S4, the obtained model parameters are stored in thesurveying instrument, that is the video-tacheometer 11, to be usedtherein to calculate for a given position on the image sensor acorresponding direction in the instrument coordinate system and if thedistance of a point imaged onto the image sensor 33 from thevideo-tacheometer is known, also corresponding Cartesian coordinates.

In section S1, for each calibration point, i.e. N times, the steps shownin FIG. 14 are executed.

First, in step S5 a new calibration point is provided by generating avirtual image of the cross-hair 78 in the collimator 68 by changing itsposition with respect to the objective 80. For that purpose, thecross-hair 78 has to be moved between the focal point of the objective80 and the objective 80 by the distance Δf.

In step S6, the distance D between the surveying instrument, that is thevideo-tacheometer 11, and the virtual calibration point is obtained. InFIG. 16 illustrates the calculation. In this Figure the first cross-hair78 is shown on the optical axis of the objective 80 for simplicity. Forcalculating the distance D, the distance s of the virtual image of thecross-hair 78 from the objective 80, more precisely the principal planeH of the objective 80 on the video-tacheometer side, is calculated fromthe focal length Δf of the objective 80 and the distance Of thecross-hair 78 from the focal point of the objective 80 by means of theformula:

$s = {f\frac{\left( {f - {\Delta \; f}} \right)}{{- \Delta}\; f}}$

The virtual image distance s is then added to the distance S_(Th/H)between the objective 80, that is its above-mentioned principal plane Hand the vertical axis of the surveying instrument, that is thevideo-tacheometer 11.

On the data processing system 65 the computer program according to thefirst exemplary embodiment of the invention is started and firstrequires to input the positive integer number N via a display and akeyboard not shown in the Figures. After inputting the integer N theprogram requests input of the distance data associated with the firstcalibration point. After input of these data, the processor 67 storesthe data in the memory 68 of the data processing system. In anotherembodiment, the number N could be pre-set in the computer program, sothat no user interaction is necessary.

In step S7, for the given calibration point different images aregenerated on the image sensor 33 and corresponding image position dataand orientation data are obtained and stored in the data processingsystem 65.

The generation of images of the calibration point as well as thegeneration of the data required for calibration are shown in more detailin FIG. 15.

The step S8, shown in FIG. 15, is performed for the first calibrationpoint. For the following calibration points, this step needs to beperformed only when necessary at least in the case that a collimator isused to provide the calibration points and that the orientation of thecollimator relative to the surveying instrument, that is thevideo-tacheometer 11, remains unchanged except for re-orientations ofthe telescope unit 16, that is the camera 19. In this step the camera 19is directed to the calibration point generated. In this embodiment, itis sufficient that an image of the calibration point appears on theimage sensor 33.

Further, the camera is brought into a first face, which means, that thevertical angle of the camera 19 is between 0 and 200 gon, 0 being thezenith as determined by the vertical circle 26.

Next, in step S9, the camera 19 is rotated and tilted to move the imageof the calibration point on the image sensor 33 to a predetermined startposition on the image sensor 33. Preferably the starting position issituated close to one of the corners of the image sensor 33. For thispurpose, the computer program stored in the data processing system 65comprises a program module for object recognition in images such asimages captured by the image sensor 33. In the memory 68 of the dataprocessing system 65 a template is stored which represents thecross-hair 78. By use of known object recognition techniques, forexample a template matching algorithm, the position of the image of thecalibration point in the captured image, that is on the image sensor 33,is obtained. The computer program now calculates whether the camera 19should be rotated by a given increment about the vertical axis 15 and/ortilted about the tilting axis 20 in order to bring the image of thecalibration point closer to the start position. It then issues acorresponding command to the surveying instrument, in which thedevice-control unit 51 receives the corresponding commands and moves thecamera 19 by the respective angles by means of the drives 22 and/or 23.Then a new image is captured and the process is repeated, until theimage of the calibration point reaches the start position. Thereby, thesize of the angle increments can be reduced as the image of calibrationpoint approaches the start position.

In step S10, the program calculates random positions in cells of amatrix covering the image sensor as target positions of images of thecalibration point. For that purpose, the image sensor is divided into anL×M matrix with predetermined positive integer numbers L and M and thegeometric centers of the cells are calculated. In FIG. 17, cells 88 arearranged in a rectangular array covering the image sensor 33. Thegeometric centers of the cells are marked by crosses. For each of thegeometric centers a for each direction in the matrix a random number isdetermined using a pseudo random number generator, the magnitude of therandom number being less than half the size of the cell in thecorresponding direction and then added to the coordinate of thegeometric center in the respective direction. The resulting randompositions in each of the cells are shown in FIG. 17 by open circles.This use of random numbers reduces the effects of defective photodetecting elements in the image sensor drastically, because it can beavoided that an image position is always on a defective pixel. Thesepositions are stored in the memory 68 of the data processing system 65.

In step S11, the telescope unit 16 and thus the camera 19 is rotated andtilted to move the image of the calibration point on the image sensor 33to the target position. For that purpose the same algorithm may be usedas in step S9. Once the image of the calibration point has reached thetarget position, the image position data, that is the coordinates x″ andy″ of the image in the image plane, are stored and the orientation data,that is the horizontal angle Hz_(m) and the vertical angle V_(m) asdetermined by the horizontal and vertical circle, respectively, are readfrom the surveying instrument in response to corresponding commands sentfrom the data processing system 65 to the surveying instrument.

After the image position data and orientation data are stored for eachtarget position, in step S12, the camera 19 is directed to thecalibration point in the second face, that is the vertical angle asdetermined by means of the vertical circle is between 200 and 400 gon.In order to ensure that an image of the calibration point will appear onthe image sensor 33 also in the second face, the camera is preferablyrotated by 200 gon about the vertical axis 5 and then tilted by 400 gonminus the vertical angle obtained for the last target position in stepS11.

The following steps S13 and S14 correspond to steps S10 and S11, theonly difference being that the camera 19 is in the second face.

Once step S15 is performed for the last of the calibration points, themodel used for calibration is provided in step S2. For that purpose, thecomputer program stored in the data processing system comprisescorresponding instructions representing the model as set out above.

The steps of section S3 are executed by means of the computer program.Once for each calibration point P_(i), i=1, N Q images j, j=1, . . . ,Q, Q being an positive integer number, are generated and correspondingimage position and orientation data are obtained by reading these data,the model parameters are adjusted so that the model predicting theposition of images of the calibration points as a function of the modelparameters, directions of the calibration points in the instrumentcoordinate system and the respective orientation data fits the measuredimage position data. The estimation method, a least squares estimate,which is equivalent to a classic adjustment method by least squares, isbased on the error function E(i, c₀, c_(F), z₀, ω, φ, κ; S₀, c_(k),x_(s), y_(s), v; {S_(l), {x″_(lj), y″_(lj), V_(mlj), Hz_(mlj)}}) givenby the following sum over all calibration points i and all images j ofthe calibration points

$E = {\sum\limits_{l = 1}^{N}{\sum\limits_{j = 1}^{Q}{\begin{bmatrix}\left( {x_{lj}^{''} - {U_{x}\begin{pmatrix}{i,c_{0},c_{F},z_{0},\omega,\varphi,{\kappa;}} \\{S_{0},c_{K},x_{S},y_{S},{v;S_{l}},V_{mlj},{H\; z_{mlj}}}\end{pmatrix}}^{2} +} \right. \\\left( {y_{lj}^{''} - {U_{y}\begin{pmatrix}{i,c_{0},c_{F},z_{0},\omega,\varphi,{\kappa;}} \\{S_{0},c_{K},x_{S},y_{S},{v;S_{l}},V_{mlj},{H\; z_{mlj}}}\end{pmatrix}}^{2}} \right.\end{bmatrix}.}}}$

Herein S_(l), {x″_(lj), y″_(lj), V_(mlj), Hz_(mlj)} denote the distancefor the calibration point l and the data sets j=1, . . . , Q for allimages of the calibration point, the data set for image j comprising theimage position data x″_(lj), y″_(lj) and the vertical and horizontalangles V_(mlj), Hz_(mlj) set.

The error function E is minimized using a suitable minimizationprocedure, for example a Gauss-Newton algorithm as described in Benning,Wilhelm: “Statistik in Geodäsie, Geoinformation and Bauwesen”,Heidelberg, Germany, 2002, ISBN 3-87907-383-X pp. 140.

In section S4, the data obtained by the computer program are stored inthe surveying instrument. For that purpose the data processing system 65sends these data via the interface 69 and the connection 72 to thesurveying instrument, i.e. the video-tacheometer 11, which stores thesedata in the non-volatile memory of the device-control unit 51 in whichalso instructions of a computer program are stored representing themodel used for calibration.

The performance of the method may be exemplified by the followingexample. In this example a variant of the method described above is usedin which, however, for each angle combination more than one measurementis made. For calibrating a camera having a focal length of 300 mm and afixed focus at 100 m, fitted to an instrument having an angle measuringaccuracy of 1″, one can use three calibration points at distances of,e.g., 20 m, 80 m and 500 m, and a total of 48 angle combinations pertelescope position, arranged in a grid of 8×6 positions, for example. If30 measurements per angle combination in which no random deviation isgreater than 0.05 pixels, are made and the corresponding data used, theinstrument can be calibrated to an accuracy of direction measurement ofapproximately 1″ in the vertical and horizontal directions. Thus, themethod is also suited for calibration of cameras having a relativelylarge focal length.

Using the model, from image position data of an image of an object pointon the image sensor, a direction of the object point with respect to theinstrument coordinate system can be calculated (see FIG. 19). Using theequation

$P_{T}^{\prime} = {\overset{\_}{O} + {R \cdot \begin{bmatrix}{x_{P}^{\prime} - {\Delta \; x^{\prime}} - x_{S}^{''}} \\{y_{P}^{\prime} - {\Delta \; y^{\prime}} - y_{s}^{''}} \\{- c_{\kappa}}\end{bmatrix}}}$

in which {right arrow over (O)} denotes a vector from the origin of theinstrument coordinate system to the projection center O, one cantransform measured image position data x′_(P), y′_(P) corresponding toan imaged object point P into the coordinate system of the instrument,i.e. video-tacheometer 11. P_(T)′ is a vector in the instrumentcoordinate system representing a direction corresponding to the measuredimage positions. The projection center O and the point P_(T)′ are bothknown in terms of coordinates with reference to the surveyinginstrument, and define an imaging ray a on which an object point beingimaged to the position on the image sensor represented by x′_(P),y′_(P). As ray does not need to intersect the video-tacheometer center,i.e. the origin of the instrument coordinate system, a distance(approximate distance) of the object point P from the video-tacheometercenter must be given for the correct calculation of a direction withrespect to the video-tacheometer center. This distance is used as aradius of a sphere extending around the video-tacheometer center, i.e.the origin of the instrument coordinate system, and intersected by theimaging ray a. In this way, two coordinate triplets are obtained, whichcan be used for direction computation, depending on the position of thetelescope unit 16 that has the function of a camera. The closer thevideo-tacheometer center is to the imaging ray, the less dependent thismethod becomes from the distance given.

With the camera calibration thus performed, it is also possible todefine a photogrammetric sighting axis as the straight line connectingthe projection center O with the instrument center formed by theintersection of the tilting axis and the vertical axis. In FIG. 19, thephotogrammetric sighting axis, shown as a dashed line, is a line coaxialwith the vector {right arrow over (O)} as the instrument center is theorigin of the coordinate system. This photogrammetric sighting axis isnot identical, though, with the actual sighting axis shown in FIG. 11.The piercing point of the photogrammetric sighting axis in the imageplane determines the position of a crosshair, at which the classicalerrors of lateral and vertical collimation are constant along thedistance. Unless they were determined during parameter estimation, thelateral and vertical deviations of the projection center can be measuredwith the pixel at which the classical errors of lateral and verticalcollimation do not change along the distance.

If an object point is sighted at with cross-hairs defined in this way,the cross-hairs, the tacheometer center, the projection center O and theobject point P would lie on a straight line, this straight line beingidentical with a photogrammetric imaging ray.

In the computer 54 of the video-theodolite 11, program code may bestored to display a mark 111, e.g. cross-hairs, indicating thephotogrammetric sighting axis on the display 53 (see FIG. 20), thecomputer thus representing a control unit for controlling the display.The corresponding position on the display 53 can be calculated eitherfrom the calibration parameters, which are stored in the instrument, orcan be calculated once and then be stored permanently in the instrument,e.g. a non-volatile memory of computer 54.

The position of the crosshairs, defined in conventional instruments asthe point in the image plane at which the lateral and verticalcollimation errors are equal to zero, can, in the same way, be assignedto a pixel on the camera's detector surface; with optical componentsless well centered, this pixel may, in the worst case, vary withdistance.

The finder camera 18 may also be calibrated using the method describedin the first exemplary embodiment, data-processing system, collimatorand computer programs. As the position of the projection center may beseen as just a set of parameters in the model, the fact that the lightpath is not straight does not require the modification of thecalibration method. This one important advantage of the invention.

In a second exemplary embodiment of the invention the method differsfrom the method described in the first exemplary embodiment in that amore detailed model for the distortions of the camera is used in whichalso terms are used which are of higher order and/or notradial-symmetric. Luhmann, Thomas: “Nahbereichsphotogrammetrie:Grundlagen, Methoden and Anwendungen”, Heidelberg, Germany, 2000, ISBN3-87907-321-X, pp. 119 to 122 disclose corresponding amendments to themodel described above.

In third exemplary embodiment of the invention, a system for calibrationschematically shown in FIG. 18 is used. This system allows anessentially automatic calibration of an instrument. The system comprisesa collimator 66′ which differs from the collimator 66 in that the mark,i.e. the cross-hair 78, may be moved by an electric drive 84 which iscontrolled via a data processing system 65′. The data processing system65′ differs from the data processing system in that it comprises anotheroutput interface 85 for outputting commands to the drive 84 of thecollimator. Further, the computer program stored in memory 68′ containsprogram code, which, when run on the processor 67 lets the processor 67issue control commands via the output interface 85 to the drive 84 tomove the cross-hair 78 into predetermined positions and to calculate thecorresponding virtual distance of the virtual calibration point.

First, a user brings the instrument in predetermined, e.g. marked,position relative to the collimator 66′, in which a virtual imagecross-hair 78 can be imaged to the image sensor 33. The position isdetermined in dependence on the properties of the collimator and of thecamera and chosen such that virtual calibration points can be providedby moving the cross-hair 78. In another variant, a mount may be used toposition the instrument in the predetermined position.

Then, the data processing system 65′ automatically carries out all stepsof sections S1 to S4 issuing commands to the surveying instrument 11, ifnecessary, receiving image position data and corresponding orientationdata from the surveying instrument 11, and performing the calculationsin step S6 and in section S3.

In a variant of this embodiment, the distances of the calibration pointscan be stored with the respective positions of the mark, so that thedistance of the virtual image of the mark does not need to be calculatedfor each calibration.

In another exemplary embodiment, the possible range of distances of atarget from the instrument is divided into a predetermined number G ofdistance subranges. The number of the distance subranges and theiractual limiting values may be chosen in dependence on the opticalproperties of the camera, in particular the camera optics and its focallength.

In each distance subrange the same model is used, however, the cameramodel parameters camera constant C_(K), the distortion parameter v, andthe offsets x_(s) and y_(s) are defined as model parameters specific foreach distance subrange. This situation is illustrated in FIG. 21, inwhich around the surveying instrument 11 G=3 different distance rangesD₁, D₂ and D₃ are partially shown. Actually, distance subrange D₃extends to infinity. Each distance subrange is defined by a minimumdistance and a maximum distance. In each of the distance subrangescalibration points 112 are provided at different distances from thesurveying instrument. FIG. 21 shows the distance subranges and thecalibration points only for visualization, actually the calibrationpoints are provided by the collimator 66′.

The model is now extended in that G different sets of camera modelparameter (S₀, c_(K), v, X_(S), y_(s))_(l), l=1, . . . G, associatedwith the distance subranges are used in dependence on the distance. Ifthe distance of a calibration point falls within one of the distancesubranges, the corresponding camera model parameters, i.e. values of thecamera model parameters, are used in the formulas for U_(x) and U_(y).

Calibration may then proceed as in the preceding exemplary embodiment,wherein after a change of distances of the calibration points the camerais re-focused. For minimization, all model parameters are adjusted, i.e.also the different sets of camera models.

After minimization, G sets of camera model parameters are obtained whichmay then be stored in a non-volatile of the surveying instrument 11. Inthe device-control unit 51 program code may be stored for calculatingvalues of the camera model parameters as a function of distance, e.g. byinterpolation between the values provided by the G camera modelparameters provided by the calibration. Then, given the distance of atarget, its coordinates or directions or bearing can be calculated as inthe first exemplary embodiment using the camera model parametersobtained from interpolation.

In a variant of last-mentioned exemplary embodiment, the focusing statusof the camera as defined by the positions of the focusing lens asdetermined in the device-control unit 51 may be used instead of thedistances. It is to be noted that the position of the focusing lens isfunction of the distance of an object point an image of which is focusedon the image sensor by motion of the focussing lens. This isparticularly preferable in the case that the surveying instrumentcomprises an autofocusing device. Then, the position of the focusinglens may be automatically provided by the autofocusing device and usedfor calculations.

A further exemplary embodiment particularly suitable for calibrating alarger number of surveying instruments of the same type is based on thethird exemplary embodiment. The distances of the calibration points,i.e. the positions of the mark or cross-hair 78, and the image positionsof images of those calibration points are predetermined and stored inthe data processing system. Thus, the distance may obtained by readingthe corresponding data from the memory of the data processing system andthe image positions need to be determined only once and can then be usedfor all instruments.

In yet another exemplary embodiment of the invention, images ofcalibration points are generated in the following way. As in the firstexemplary embodiment, the camera is oriented to the calibration point sothat the image of the calibration point is in the start position.However, in the present exemplary embodiment, the horizontal andvertical angles are set according to predetermined combinations ofvalues. If the field of view is narrow, as the case for the telecamera19, the angles may be given at constant intervals. These values may bechosen so that assuming no axis errors and an ideal camera havingdesired optical properties, the resulting image points are distributedhomogeneously all over the image sensor. The actual distribution maydiffer due to the tolerances of the axes of the actual instrument andthe optical properties of the actual camera. After setting these angles,the image position data are determined, e.g. again using objectrecognition, and stored together with the orientation data comprisingthe horizontal and vertical angles. The estimation of the modelparameters, i.e. the minimization, is performed as in the firstexemplary embodiment.

In a variant of this exemplary embodiment, for each combination ofhorizontal and vertical angles to be set according to the horizontal andvertical circles, the positions of image points of the calibrationpoints on the image sensor are obtained in both faces of the instrument.I.e. if a horizontal angle is Hz_(l) and a vertical angle is V_(l) inthe first face, the camera is set to a second horizontal angleHz_(ll)=200 gon+Hz_(l) and an vertical angle V_(ll)=400 gon−V_(l), ifthe zenith corresponds to 0 gon. In another preferred exemplaryembodiment as calibration points triple reflectors in differentdistances from the surveying instrument may be used. The distance datamay be obtained using the distance measuring device 30.

The invention can also be used with a video-tacheometer with a telescopeunit 16′ shown in FIG. 21 which differs from the above-mentionedtelescope unit 16.

It comprises a telescope 89 formed by an objective 31 as in the firstexemplary embodiment, a focusing lens 91, a reversing prism 92, across-hair 93 and an eyepiece 94. An image is focused onto thecross-hair 93 by shifting the focusing lens 91 along the optical axis ofthe telescope as indicated by the arrows in FIG. 20. The telescope isused for sighting at a target.

A further device in the telescope unit 16′ is constituted by thetracking device or tracker, respectively, which serves to automaticallysight a reflector located in the target point and to track it, when itis being carried from one point to another. The tracker comprises atransmitter, which emits a narrow bundle of optical radiation; theobjective 31 through which the bundle is incident in the direction oftransmission and, after reflection at the target, in the receivingdirection; receiving optics; a receiver 95, which detects the positionof the bundle reflected back by the target and focused onto it by thereceiving optics, and a closed-loop control which guides the telescopeunit 16′ or the alidade 12, respectively, such that the position of theray bundle reflected back by the target remains constant on the receiver95.

More precisely, the transmitter of the tracker comprises a radiationsource 96 for emitting optical, preferably infrared, radiation, such asa laser diode, for example, and transmitting optics, which comprisefirst collimating optics 97 and a prism 98, at the oblique surface ofwhich the ray bundle coming from the radiation source 96 and collimatedby the first collimator optics 97 is reflected in the direction of theoptical axis of the objective 31. The receiving optics are formed by asplitting prism 99 and second collimator optics 100. Finally, thereceiver 95 comprises several detection elements which are sensitive tothe radiation from the transmitter. For the receiver 95, use may be madeof a quadrant diode or of a camera circuit, for example.

The transmitter of the tracker transmits the ray bundle, which has beenemitted by the radiation source 96, collimated by the first collimatoroptics 97 and deflected onto the optical axis of the objective 31 by theprism 98, to the target, through the center of the objective 31. The raybundle is reflected back to the tacheometer by the target, for example atriple mirror or reflector, respectively, and then enters the telescopeunit 16′ again, through the objective 31. On its way to the target andback, the ray bundle, which was narrow at first, has broadened so much,at a sufficiently great distance from the target, that it fills theentire diameter of the objective 31 upon its return, so that those partsof the ray bundle which are not incident on the prism 98 and are passinga dichroic mirror 101. The wavelength of the ray bundle emitted by thetransmitter is selected such that the ray bundle passes the dichroicmirror 101 without substantial reflection, so that said mirror haspractically no influence on said bundle. The ray bundle, having passedthrough the dichroic mirror 101, then enters the splitting prism 99. Thesplitting layer thereof selectively reflects at the wavelength of theradiation emitted by the transmitter, so that it deflects the raybundle, which has entered the splitting prism 99, in the direction ofthe second collimator optics 100, but allows visible light to pass. Thesecond collimator optics 100 focus the ray bundle from the transmitter,said bundle having been reflected by the target, onto the receiver 95 ofthe tracker. If the position of the image of the target on the receiver95 deviates from a predetermined position, e.g. in the center, thetracker supplies a signal concerning amount and direction of suchdeviation to the device-control computer (not shown in FIG. 4), whichcontrols the drives, so as to rotate the telescope unit 16′, togetherwith the alidade 12, if required, such that the image on the receiver 95is at the predetermined position again, which is in the center in theexample.

Further, a finder camera 102 is provided in the telescope unit 16′. Thefinder camera 102 comprises a camera objective 103 and an image sensor104. Signals of the image sensor 104 are processed by an imageprocessing circuit 105 which is connected to the device-control unit 51.The finder camera 102 can be used to find a target to be measured moreeasily. The finder camera 102 can be calibrated using the same method asdescribed in the first exemplary embodiment as the projection center ofthe pinhole camera model can in principle be located arbitrarily withrespect to the vertical axis.

The distance-measuring device 106 measures the distance from a target tothe tacheometer by directing radiation to the target and receiving theradiation reflected back by it. The distance-measuring device 106 isformed by components of the telescope and by further components. Aninfrared-light source, which is not explicitly shown in FIG. 20 andemits infrared radiation in a pulsed manner within a predeterminedwavelength range, for example a laser diode, directs infrared radiation,after focusing by transmitting/receiving optics 107, to a surface of theprism 108, which is reflective for the light from the infrared lightsource, and passes it from there to the dichroic mirror 101, which isreflective for the infrared light from the infrared-light source of thedistance-measuring device 106 and, therefore, deflects the infraredlight onto the objective 31. The infrared-light source and thetransmitting/receiving optics 107 are arranged and formed such that theray bundle emitted by the infrared-light source is focused along theoptical path of the distance-measuring device 106, at a distance fromthe objective 31 which is the focal width of the objective 31, and thus,a near-parallel ray bundle is emitted by the objective 31, said raybundle then impinging on a target, such as a reflector, for example atriple mirror, or also a natural target, e.g. the wall of a house. Thereflected ray bundle passes back along the same path from the target,via the objective 31, the dichroic mirror 101 and the surface 108 of theprism 98, to the transmitting/receiving optics 107, which focus the raybundle onto a receiving element (not shown in FIG. 20) of thedistance-measuring device 106, which detects the radiation. The distanceto the target is then determined from the transit time of a pulsebetween emission and reception, which transit time has been determinedby means of a corresponding electronic circuit. Since the ray bundle isemitted along the optical axis of the objective 31, the distance to atarget sighted by means of the telescope is determined on the opticalaxis.

Several aspects of the invention may be seen from another point of viewas set out below. Therein, the terms tacheometer and tachymeter are usedas synonyms.

Surveying increasingly makes use of video surveying instruments,especially video tachymeters or video theodolites, i.e. tachymeters ortheodolites equipped not with an eyepiece but with a cameraincorporating a spatially resolving detector array. The use of suchcameras involves the problem of calibration, as the so-called interiorand exterior orientation of the camera is unknown. The interiororientation is defined by two mutually orthogonal axes in the imageplane and an axis normal to these extending from the origin to aneye-point or projection center O, in which all rays originating fromobject points intersect, and a coordinate system resulting therefrom.The position of this coordinate system relative to that of the surveyinginstrument is described by the exterior orientation, which allows forthree translations and three rotations. As a rule, the camera will havea near-optimum alignment, with the perpendicular dropped from theprojection center O onto the image plane coinciding with the opticalaxis of the instrument's telescope system, but in surveying instrumentsof the type mentioned above, maximum accuracy is of the essence, sothat, e.g., residual errors of adjustment call for calibration, i.e. adetermination of the camera model and the position of the camerarelative to the instrument to which it is attached.

To calibrate cameras per se, the prior art uses photogrammetric methods.The presently most common method of camera calibration in terrestrialphotogrammetry is known as simultaneous calibration. With this method,the calibration parameters of the camera are determined together withthe evaluation of object information. The basis for image dataevaluation and calibration, respectively, is an analytical model.Another method of camera calibration uses a test field. Such a testfield has signalized targets, e.g., illuminated object points, thecoordinates and/or scale data of which are known. The test field usuallyhas three dimensions and is photographed using different capturingconfigurations, i.e. positions of the camera relative to the test field.Just like the method of simultaneous calibration, the method of cameracalibration by means of a test field is based on an analytical model. Inthis model, the parameters of the orientations are determined from thefunctional relationship between object information and imagecoordinates. For this, one requires suitable geometries of intersectionof the imaging rays or the capturing geometries and the spatialextension of the field with the object points. The larger and especiallythe deeper the space available for the object points, the greater is theaccuracy and reliability with which the camera can be calibrated. It isof advantage to make redundant measurements, i.e. to collectobservations in excess of the number of parameters to be determined. Bymeans of an adjustment procedure, the parameters can then be determinedwith greater reliability. An adjustment procedure that is wellestablished in geodesy is the least-squares method.

The basis of any analytical model is provided by what is known ascollinearity equations, which establish the functional relationshipbetween the coordinates (X,Y,Z) of an object point in a so-calledexterior space and the image coordinates (x′,y′,−c_(K)) of the image ofthe object point in the so-called interior space, a coordinate systemthat describes the interior orientation of the camera. c_(K)is known asthe calibrated focal length or also as the camera constant, the absolutevalue of which may be comparable to the focal length f of the imagingoptics. For the x′ and y′ image coordinates in the interior coordinatesystem, the collinearity equations are

$x^{\prime} = {x_{0}^{\prime} - {c_{K}\frac{{r_{11}\left( {X - X_{0}} \right)} + {r_{21}\left( {Y - Y_{0}} \right)} + {r_{31}\left( {Z - Z_{0}} \right)}}{{r_{13}\left( {X - X_{0}} \right)} + {r_{23}\left( {Y - Y_{0}} \right)} + {r_{33}\left( {Z - Z_{0}} \right)}}} + {\Delta \; x^{\prime}}}$$y^{\prime} = {y_{0}^{\prime} - {c_{K}\frac{{r_{12}\left( {X - X_{0}} \right)} + {r_{22}\left( {Y - Y_{0}} \right)} + {r_{32}\left( {Z - Z_{0}} \right)}}{{r_{13}\left( {X - X_{0}} \right)} + {r_{23}\left( {Y - Y_{0}} \right)} + {r_{33}\left( {Z - Z_{0}} \right)}}} + {\Delta \; y^{\prime}}}$

The coordinates (X₀,Y₀,Z₀) indicate the position of the eye-point orprojection center O in the exterior space, which is, at the same time,the origin of the image coordinate system. The magnitudes r_(ij) withi,j=1, . . . , 3 are elements of a rotation matrix R, which describesthe rotation of the image coordinate system relative to the exteriorcoordinate system. In this way, the coordinates (X,Y,Z) of a point inthe exterior space can be transformed into image coordinates. Reversely,object coordinates cannot be computed from image coordinates unlessfurther information is known, such as, e.g., the distance of the objectpoint from the position of the camera at the time of image-capturing.The coordinates x′₀ and y′₀ describe the position of the so-calledprincipal point in the image plane of the camera. This is defined by thepiercing point along the perpendicular connecting the image plane withthe projection center O. Allowance for the camera lens is made by thecalibrated focal length c_(K) on the one hand, and by the distortionparameters Δx′, Δy′ that reflect the imaging errors of the camera opticson the other hand.

If a camera is used in a surveying instrument such as a tachymeter ortheodolite, the known photogrammetric methods cannot be used readily, asin addition to the parameter of interior and exterior orientation thereare instrument-specific parameters and possibly also errors of theinstrument axes. In case a tachymeter is used, the bearing measurementsmade with the instrument have to be included in the calibration.Approaches to this problem are also known in the prior art; arguably theclosest prior art is in an article by Y. D. Huang, “Calibration of theWild P32 Camera using the Camera-ON-Theodolite method”, published inPhotogrammetric Record, 16(91), 1998. Huang connects one or maximallytwo reference points arranged at different distances to the instrument(this term denotes the system consisting of the surveying instrumentproper and the camera). These reference points are observed with thecamera to be calibrated, at different instrument directions, i.e.different combinations of horizontal and vertical angles to be set onthe instrument. As Huang uses a theodolite, the distance between the twopoints, or the distances between the points and the instrument must beknown. The drawback of Huang's method is that instrument errors such astilting axis and lateral collimation errors remain unconsidered.Calibration errors are larger depending on the magnitude of theseinstrument errors, which diminishes the overall accuracy of theinstrument.

Departing from this state of prior art, the problem underlying theinvention is to develop an improved method for calibrating a surveyinginstrument equipped with a camera that comprises a spatially resolvingdetector array.

Given a method for calibrating a surveying instrument equipped with acamera incorporating a spatially resolving detector array, in which thesurveying instrument is used for successively sighting given referencepoints P_(i) with i=1, . . . , N and a positive integer N, to establishthe distance to each reference point P_(i), to determine, in a firstposition or first face, the image coordinates of the image of thereference point P_(i) in the camera's image plane for differentcombinations of horizontal angles Hz_(l) and vertical angles V_(l) to beset on the instrument, to save these image coordinates in associationwith the respective angle combination (Hz_(l), V_(l)), and in which anadjustment procedure is used to establish the position of the camerarelative to the surveying instrument from the saved data, this problemis solved in such a way that, for each of the angle combinations, asecond position or second face is set by turning the surveyinginstrument about a vertical axis by 200 gon and setting it to ahorizontal angle Hz_(ll), and by turning the camera about a horizontaltilting axis and setting it to a vertical angle V_(ll), with V_(ll)=400gon−V_(l). A vertical angle of 0 gon corresponds to sighting of thezenith. In the second position or face, again the image coordinates ofthe reference point P_(i) are determined and saved in association withthe respective angle combination (Hz_(ll), V_(ll)). Finally, calibrationis effected using the data of the angle combinations saved in bothpositions or faces, respectively, i.e. the image coordinates saved inassociation with the respective angle combination.

In other words, there is provided a method for calibrating a surveyinginstrument equipped with a camera comprising a spatially resolvingdetector array, in which the surveying instrument is used to sight, insuccession, predetermined reference points (P_(i)), with i=1, . . . , Nand a natural number (N), for each reference point (P_(i)), the distanceis determined and, in a first position or face, the image coordinates ofthe image of the reference point (P_(i)) in the image plane of thecamera are determined for different given combinations of horizontalangles (Hz_(l)) and vertical angles (V_(l)) to be set on the surveyinginstrument, and saved in association with the respective anglecombination (Hz_(l), V_(l)), and the position of the camera relative tothe surveying instrument is determined by means of an adjustmentprocedure on the basis of the saved data, characterized in that, foreach of the angle combinations, a second position or face is set byturning the surveying instrument by 200 gon about a vertical axis andsetting it to a horizontal angle (Hz_(ll)), and by turning the cameraabout a horizontal tilting axis and setting it to a vertical angle(V_(ll)) with V_(ll)=400 gon−V_(l), with a vertical angle of 0 goncorresponding to a sighting of the zenith, and in that, in the secondposition or face likewise, the image coordinates of the image of thereference point (P_(i)) are determined and saved in association with therespective angle combination (Hz_(ll), V_(ll)), and in that thecalibration is performed using the data saved for both positions orfaces.

In the first position or face, a horizontal angle Hz, and a verticalangle V_(l) are set on the instrument. For setting the second positionor face, the instrument is first turned out of the originally sethorizontal angle Hz_(l) by 200 gon, i.e. a half circle, and thus thehorizontal angle Hz_(ll) is set in the second position or face. Afterthis, the vertical angle V_(ll) is set in accordance with the equation

V _(ll)=400 gon−V _(l)

This allows for the fact that the scale by which the vertical angle isset takes part in the rotation of the vertical axis. In this procedure,the zero point of the vertical angle scale, i.e. the point at which thevertical angle is 0 gon, has been positioned to the zenith, which meansthat the camera optics faces vertically up if this angle is set.

In this procedure it does not matter whether the second position or faceis set directly after measuring in the first position or face for eachof the angle combinations, or whether one takes all measurements in thefirst position or face, followed by all measurements in the secondposition or face. In general, the latter option should be preferred, asthe instrument is less stressed by wide-range rotations.

Together with an extended mathematical model, this method allows toachieve higher accuracy in calibration. The basis here again is formedby the collinearity equations, with the difference that both theprojection center and the object point in the exterior space aredescribed in terms of polar coordinates. The additional parametersresulting from the use of the surveying instrument are partially allowedfor in the photogrammetric model by further rotation matrices, themultiplication of which yields the total rotation matrix. As the camerais rigidly connected with the surveying instrument, the camera takespart in the rotations of the instrument about the vertical axis and/orhorizontal tilting axis. As the surveying instrument is provided with anangle measuring system, two rotation angles are measured directly. It isfurther necessary to allow for constant angular deviations, which havethe effect of rotations. These include the instrument's tilting axiserror, which occurs if the tilting is not at right angles with thevertical axis, and a lateral deviation of the projection center from thetheoretical sighting axis, the effect of which corresponds to that of alateral collimation error.

In a preferred embodiment of the invention, the reference points P_(i)are given or located, at different distances from the surveyinginstrument. In this way, the accuracy of calibration can be furtherincreased. The accuracy of the method is the higher, the farther thepoints are spaced from each other in spatial depth.

In a particularly preferred embodiment of the method, the referencepoints P_(i) are given or located, by means of a collimator and afloating mark that can be shifted between the collimator lens orcollimator objective and its focal point. The prior art frequently usescollimators together with geodesic instruments for adjusting andmeasuring procedures. Collimators are characterized in that they emitparallel light rays and project a point lying at optical infinity into afinite distance. The floating mark—cross-hairs, a slit or a stop of someother shape—is provided at the collimator's focal point. In case of acollimator having an extension, the floating mark can be shifted betweenthe collimator lens or objective and the focal point of the collimatorlens or objective. The amount of shift can, as a rule, be read tomicrometer accuracy. From the amount of shift relative to the focalpoint and the focal length, one can determine the image distance of thevirtual, erect image. This image is now observed with the surveyinginstrument to be calibrated. From the sum of the distance from thevertical axis of the instrument to the principal focal plane of thecollimator lens or objective and the image distance there results thefinal distance between the instrument and the virtual reference pointcreated by the collimator. A collimator can thus be used to createreference points at distances as large as 2000 m or more, whereas it isdifficult to create reference points at such distances without acollimator: It is difficult enough to find such a distance that is freefrom sighting obstacles; additional factors that can impair themeasurements are atmospheric phenomena like air turbulence. Moreover,reference points of different sizes would be needed for differentdistances in order to obtain respective image points approximately equalin size. Calibration by means of a collimator is therefore particularlysuitable for calibration of finished instruments by the manufacturer, asit takes little space and can be largely automated. Finally, this methodmakes calibration independent of environmental conditions, as thespatially resolving detector array of the camera, which, as a rule, iscomposed of pixels, is frequently subject to influences by ambientlight.

In another embodiment of the method, the angle combinations arepredetermined or given by a grid. The grid is chosen so that, whenpositions are set that represent the angle combinations, the referencepoints are distributed as homogeneously as possible all over the imageplane.

In yet another embodiment of the method, for each of the anglecombinations corresponding to a position in the grid, setting of thesurveying instrument to this position includes the determination of, andallowing for, a random deviation from this position. The randomdeviation may be smaller, in any direction, than half the distancebetween two grid positions in that direction. In this way, a possiblyexisting systematic error, which would be detected only during theadjustment computation, can be reduced. It is expedient not to allow theerrors to be greater than half the distance between two adjacent gridpositions in either direction, or else the homogeneity of distributionof the images of the reference points would be substantially impaired.The random errors of each angle combination need not be equal for thefirst and second positions or faces and may be determined separately.I.e., for each angle combination, the random deviations may bedetermined separately for the first and second positions or faces. Thedetermination may be effected, e.g., by computation using a sequence ofpseudo-random numbers.

If a tachymeter is used, it is of advantage to determine the distance tothe reference points P_(i) by means of electro-optical distancemeasurement.

Hereinafter, another exemplary embodiment of the invention is describedin detail with reference to an embodiment example in the form of atachymeter and with reference to the drawings 23 to 26.

FIG. 23 schematically shows, first of all, the design of a tachymeterthat can be used for performing the method according to the invention.Arranged on a fixed lower part 201 supported by a tribrach, an upperpart 202—shown in a sectional view here—can be rotated about thevertical axis via a bearing 203. Rotation of the upper part 202 can beeffected by means of a horizontal drive 204. The angle Hz_(l) or Hz_(ll)set on a horizontal graded circle 205 is automatically recorded througha horizontal sensing head 206 and transmitted to a control and dataanalysis unit (not shown). Also shown is a telescope body 207 having thefunction of a camera, which is mounted rotatable about the tilting axisvia a bearing 208 connected with the upper part 202. The telescope body207 contains an objective 209, a focusing lens, and a detector array,for example a CCD array. Rotation of the telescope body 207 can beeffected by means of a vertical drive 210. The angle V_(ll) or V_(ll)set on a vertical graded circle 211 is transmitted to the control anddata analysis unit via a vertical sensing head 212.

FIG. 24 shows the image coordinate system with the coordinates(x′,y′,−c_(K)) as related to the superordinate coordinate system(X,Y,Z). The drawing shows the origin of the superordinate coordinatesystem as lying at the center of the horizontal circle on which thehorizontal angle set on the tachymeter or theodolite is read, as thesaid coordinate system does not change its position in space; actually,however, the said origin lies at the intersection of the vertical,tilting and sighting axes (tachymeter center). The Z axis of thesuperordinate system coincides with the vertical axis of the instrument,and the Y axis coincides with the zero direction marked on thehorizontal circle. The origin of the image coordinate system is theprincipal point H′ having the coordinates x′₀ and y′₀ in the imageplane; this principal point is defined by the piercing point of aconnection line to the projection center O, this line being normal tothe image plane. Also shown are three rotations with angles κ, φ, ω,which are independent of any errors and directions of the tachymeter andare essentially given by the mounting of the camera relative to thesighting optics. They are described by the rotation matrix

$\left( {{R_{\omega}(\omega)} \cdot {R_{\varphi}(\varphi)} \cdot {R_{\kappa}(\kappa)}} \right) = \begin{bmatrix}{{\cos (\varphi)}{\cos (\kappa)}} & {{- {\cos (\varphi)}}{\sin (\kappa)}} & {\sin (\varphi)} \\\begin{matrix}{{\cos (\omega){\sin (\kappa)}} +} \\{\sin (\omega){\sin (\varphi)}{\cos (\kappa)}}\end{matrix} & \begin{matrix}{{\cos (\omega){\cos (\kappa)}} -} \\{\sin (\omega){\sin (\varphi)}{\sin (\kappa)}}\end{matrix} & {{- {\sin (\omega)}}{\cos (\varphi)}} \\\begin{matrix}{{\sin (\omega){\sin (\kappa)}} -} \\{\cos (\omega){\sin (\varphi)}{\cos (\kappa)}}\end{matrix} & \begin{matrix}{{\sin (\omega){\cos (\kappa)}} +} \\{\cos (\omega){\sin (\varphi)}{\sin (\kappa)}}\end{matrix} & {{\cos (\omega)}{\cos (\varphi)}}\end{bmatrix}$

The distance between the principal point H′ and the projection center Ois the calibrated focal length c_(K).

The Z axis intersects the tilting axis about which the verticalrotations take place. Because of the tilting axis error, the realtilting axis, shown in FIG. 24 as a solid line, deviates from thetheoretical tilting axis shown as a dashed line. The angular deviationbetween the non-orthogonality of the tilting axis and the instrument'svertical axis is designated i. Likewise, the real sighting axis, whichcorresponds to the direction of image capturing and is shown in thedrawing as −z′ axis of the image coordinate system, deviates from thetheoretical sighting axis, which is shown as a broken line. As,furthermore, the projection center O does not coincide with theinstrument center, which is defined by the point of intersection of thevertical and tilting axes, further parameters have to be introduced tocomplete the model and obtain the complete rotation matrix: Theparameter S₀ describes the oblique distance from the instrument centerto the projection center O. The parameter c₀ describes the angulardeviation of the projection center O from the theoretical sighting axisthat is orthogonal with the tilting axis, and the parameter z₀ describesthe vertical angular deviation of the projection center O from anoriented theoretical sighting axis. Further important quantities areexplained in FIG. 25 and FIG. 26. Shown in FIG. 25 is the horizontalangle Hz_(l/ll) read off the instrument, the index “l/ll” meaning thatthis may be either the horizontal angle Hz, read in the first positionor face or the angle Hz_(ll) read in the second position or face. Thevalue of the horizontal angle Hz_(l/ll) depends on the position of thesensing head inside the instrument, which is marked here by the distancea. The angle c_(F) is the angular deviation of the mechanical axis ofthe telescope body from the theoretical sighting axis, i.e. the angulardeviation from orthogonality with the tilting axis. The mechanical axisof the telescope body is defined by the centricity of the opticalcomponents such as objective, sliding lens and eyepiece. In case of theoptical components being ideally centered and aligned, this axiscoincides with the optical axis of the telescope body. c_(F) acts like aclassical lateral collimation error; it acts exclusively on the camera,and not on the projection center. Also shown in the drawing are anobject point P and its corresponding image point P′ in the image planewith the coordinates (x′_(P′),y′_(P′),−c_(K)). Finally, shown in FIG.26, which shows the vertical plane, is the vertical direction V_(l/ll)read off relative to the vertical axis; this direction is shown in theform of an angle. Here again, the index “l/ll” means that this may beeither the vertical angle V_(t) read in the first position or face orthe vertical angle V_(ll) read in the second position or face.

With these designations, the coordinates of the projection center Oresult as

$O = {\begin{bmatrix}X_{0} \\Y_{0} \\Z_{0}\end{bmatrix} = \begin{bmatrix}{S_{0} \cdot {\sin \left( {V_{I/{II}} + z_{0}} \right)} \cdot {\sin \begin{pmatrix}{{H\; z_{I/{II}}} + \frac{c_{0}}{\sin \left( {V_{I/{II}} + z_{0}} \right)} +} \\{i \cdot {\cot \left( {V_{I/{II}} + z_{0}} \right)}}\end{pmatrix}}} \\{S_{0} \cdot {\sin \left( {V_{I/{II}} + z_{0}} \right)} \cdot {\cos \begin{pmatrix}{{H\; z_{I/{II}}} + \frac{c_{0}}{\sin \left( {V_{I/{II}} + z_{0}} \right)} +} \\{i \cdot {\cot \left( {V_{I/{II}} + z_{0}} \right)}}\end{pmatrix}}} \\{S_{0} \cdot {\cos \left( {V_{I/{II}} + z_{0}} \right)}}\end{bmatrix}}$

These are then used in the collinearity equations.

To obtain a rotation matrix for the total rotation of the imagecoordinate system of the camera built into the instrument, sevenrotations are executed in succession. The first rotation is that of thealidade, i.e. that of the instrument about the vertical axis. Thisrotation is indirectly combined with the angle Hz_(l/ll). Here it isnecessary, however, to make allowance for the influences of a potentialerror of the instrument's tilting axis, described by the angle i, and ofthe deviation c_(F), of the axis of the telescope body fromorthogonality with the tilting axis. This results in an improvedhorizontal angle Hz_(K):

${H\; z_{K}} = {{H\; z_{I/{II}}} + \frac{c_{F}}{\sin \left( V_{0} \right)} + {i \cdot {\cot \left( V_{0} \right)}}}$

V₀=V_(l/ll)+z₀ designates the vertical angle of the projection center.If rotation by the angle —Hz_(K) takes place about the z′ axis of theimage coordinate system, the resulting rotation matrix is:

$R_{\kappa} = {\left( {H\; z_{K}} \right) = \begin{bmatrix}{\cos \left( {{- H}\; z_{K}} \right)} & {\sin \left( {{- H}\; z_{K}} \right)} & 0 \\{- {\sin \left( {{- H}\; z_{K}} \right)}} & {\cos \left( {{- H}\; z_{K}} \right)} & 0 \\0 & 0 & 1\end{bmatrix}}$

With the rotation of the alidade about the vertical axis completed, andwith no further mechanical movement taking place, a tilting axis erroracts on the image coordinate system as a rotation.

This rotation is executed as a second rotation by the angle i about they′ axis, which took part in the first rotation. Assuming that thetilting axis is, in this constellation, approximately parallel with thex′ axis, the resulting rotation matrix is

${R_{\varphi}(i)} = \begin{bmatrix}{\cos (i)} & 0 & {\sin (i)} \\0 & 1 & 0 \\{- {\sin (i)}} & 0 & {\cos (i)}\end{bmatrix}$

The next rotation to be considered is that of the image coordinatesystem by the vertical angle. This rotation can be directly related tothe direction V_(l/ll) measured on the instrument, allowing for thecorrection z₀. As a matter of principle, the image coordinate system isrotated by 200 gon about the x′ axis. The rotation matrix is

${R_{\omega}\left( V_{0} \right)} = \begin{bmatrix}1 & 0 & 0 \\0 & {\cos \left( {{200\; {gon}} - V_{0}} \right)} & {- {\sin \left( {{200\; {gon}} - V_{0}} \right)}} \\0 & {\sin \left( {{200\; {gon}} - V_{0}} \right)} & {\cos \left( {{200\; {gon}} - V_{0}} \right)}\end{bmatrix}$

The next rotation, which again acts internally only, is effected by thedeviation c_(F) of the axis of the telescope body. The rotation matrixin this case is

${R_{\varphi}\left( c_{F} \right)} = \begin{bmatrix}{\cos \left( c_{F} \right)} & 0 & {\sin \left( c_{F} \right)} \\0 & 1 & 0 \\{- {\sin \left( c_{F} \right)}} & 0 & {\cos \left( c_{F} \right)}\end{bmatrix}$

This is followed by the three rotations about the angles κ, φ and ωmentioned above, which again are internal only. The total rotationmatrix R then results from successive multiplication of the rotationmatrices in the correct order, viz.:

R=R _(κ)(Hz _(K))·R _(φ)(k ₀)·R _(ω)(V ₀)·R _(φ)(C _(F))R _(ω)(ω)·R_(φ)(φ)·R _(κ)(κ)

In this way, it is possible to describe the rotations of a cameraintegrated in the instrument arbitrarily, consideringinstrument-specific parameters and with the aid of a directionmeasurement. The elements r_(i,j) of the rotation matrix R are also usedas input quantities for the collinearity equations.

If, for calibrating a camera having a focal length of 300 mm and a fixedfocus at 100 m, fitted to an instrument having an angle measuringaccuracy of 1″, one uses three points at distances of, e.g., 20 m, 80 mand 500 m, and a total of 48 angle combinations per telescope position,arranged in a grid of 8×6 positions, with 30 measurements per anglecombination in which no random deviation is greater than 0.05 pixels,the instrument can be calibrated to an accuracy of direction measurementof approximately 1″ in the vertical and horizontal directions. Attemptsto calibrate long-focus cameras by conventional calibration methods havefailed so far.

It should be noted here that this way of calibration also allowsinstrumental directions to be derived from the image coordinates. Thusit is possible to carry out a direction measurement outside the sightingaxis. Due to this calibration, the projection center can be computed interms of Cartesian coordinates in any position of the instrument. Usingthe formula

$P_{T}^{\prime} = {\overset{\_}{O} + {R \cdot \begin{bmatrix}{x_{P}^{\prime} - {\Delta \; x^{\prime}}} \\{y_{P}^{\prime} - {\Delta \; y^{\prime}}} \\{- c_{K}}\end{bmatrix}}}$

it is possible to transform measured image coordinates into thecoordinate system of the tachymeter. P_(T)′ is a vector with themeasured image coordinates transformed into the tachymeter coordinatesystem. The projection center O and the point P_(T)′ are both known interms of coordinates with reference to the tachymeter, and define animaging ray g. As this does not intersect the tachymeter center, adistance (approximate distance) of the object point P from thetachymeter center must be given for the strict direction derivationreferenced to the tachymeter center. This distance is used as the radiusof a sphere extending around the tachymeter center and intersected bythe imaging ray g. In this way, two coordinate triplets are obtained,which can be used for direction computation, depending on the positionof the telescope body that has the function of a camera. The closer thetachymeter center is to the imaging ray, the less dependent this methodbecomes from the distance given.

Although the method was explained above using a tachymeter, it can alsobe used with other surveying instruments such as theodolites orso-called scanners, provided that they satisfy the prerequisitesdescribed herein.

With the camera calibration thus performed, it is also possible todefine the photogrammetric sighting axis, namely, as the straight lineconnecting the projection center O with the instrument center formed bythe intersection of the tilting and vertical axes. This sighting axis isnot identical, though, with the actual sighting axis shown in FIG. 25.The piercing point of the photogrammetric sighting axis in the imageplane determines the position of cross-hairs, at which the classicallateral collimation error and vertical height index error are constantalong the distance. Unless they were determined during parameterestimation, the lateral and vertical deviations of the projection centercan be measured with that pixel at which the classical errors of lateraland vertical collimation do not change along the distance.

If an object point were sighted with cross-hairs defined in this way,the cross-hairs, the tachymeter center, the projection center O and theobject point P would lie on a straight line, this straight line beingidentical with a photogrammetric imaging ray.

The position of the cross-hairs, defined in conventional instruments asthat point in the image plane at which the lateral collimation error andvertical height index error are equal to zero, can, in the same way, beassigned to a pixel on the camera's detector surface; with opticalcomponents less well centered, this pixel may, in the worst case, varywith distance.

1-27. (canceled)
 28. A surveying instrument having a camera with an image sensor, wherein imaging of an object point by the camera on the image sensor can be modeled by use of a camera model having a projection center, a display for displaying images based on images captured by the image sensor, and a control unit for controlling the display to display a mark indicating a sighting axis, the sighting axis being defined by a line connecting (1) the projection center, and (2) the intersection point or point of closest approach of the tilting axis and the vertical axis.
 29. A surveying instrument comprising a base element and a camera with an image sensor, the camera being rotatable about a vertical axis fixed with respect to said base element and being rotatable about a tilting axis, the tilting axis being rotated about the vertical axis with rotation of the camera about the vertical axis, wherein imaging of an object point on the image sensor by the camera can be modeled by use of a camera model working in a coordinate system fixed to the camera and a transformation model for transforming coordinates between an instrument coordinate system and the camera coordinate system, the instrument further comprising a display and a data processing unit, in which program code is stored for determining a direction of an object point captured by the camera using the camera and transformation models and for displaying the direction of the object point, wherein a direction from the origin of the instrument coordinate system to the object point is calculated using a direction obtained by means of the camera model and the transformation model and the distance of the object point from the origin of the instrument coordinate system.
 30. A computer program for a surveying instrument, the surveying instrument comprising a data processing system, a display, a base element and a camera with an image sensor, the camera being rotatable about a vertical axis fixed with respect to said base element and being rotatable about a tilting axis, the tilting axis being rotated about the vertical axis with rotation of the camera about the vertical axis, wherein imaging of an object point on the image sensor by the camera can be modeled by use of a camera model working in a coordinate system fixed to the camera and a transformation model for transforming coordinates between an instrument coordinate system and the camera coordinate system, the computer program comprising program code for determining and displaying a direction of an object point captured by the camera using the camera and transformation models, wherein a direction from the origin of the instrument coordinate system to the object point is calculated using a direction obtained by means of the camera model and the transformation model and the distance of the object point from the origin of the instrument coordinate system when the program is executed by the data processing system. 